NEVERTHELESS DEATH REIGNED FROM ADAM UNTIL MOSES: all ebasileusen (3SAAI) o thanatos apo adam mechri moseos: (Ro 5:17,21; Ge 4:8; 5:5-31; 7:22; 19:25; Ex 1:6; Heb 9:27)

Donald Barnhouse notes that...

About a year before Paul wrote the epistle to the Romans, he wrote his first letter to the Corinthians in which he spoke of the Lord Jesus as “the last Adam,” and “the second man” (1 Cor. 15:45, 47). There he presented, in outline, the truth on which he elaborates in Romans. “As in Adam all die; so also in Christ shall all be made alive” (1 Cor. 15:22). He presents death as an enemy to destroy (v. 26); and He presents Christ as reigning, and continuing His reign until all things, including the subversive reign of death, are put under His feet (vv. 24, 25, 27). The first Adam is presented as a living soul; the last Adam as a life giving spirit (v. 45). Now in Romans, this theme is greatly enlarged and its implications made plain in practical application to the Christian’s daily life and walk. Here, in the argument of this epistle, we are at a turning point (Romans 5:12-21), for it concerns the active Christian life and the life of Christ flowing through us, that we may know constant triumph in Him. (Barnhouse, D. G.. God's Grace: Romans 5:12-21. Grand Rapids, MI.: William B. Eerdmans Publishing Company)

Hodge writes that...

men were subject to death before the law of Moses was given, and consequently not on account of violating it. Therefore there must be some other reason for their exposure to death.

Nevertheless - a strong adversative. Paul is saying is that far from sin not being credited when there is no law, nevertheless death reigned.

Death (2288) (thanatos) indicates the opposite of life and the absence of life and in the NT is seen as the consequence and punishment of sin. Death speaks of separation, physically of the soul from the body and spiritually of the soul from God. Note that death does not signify either annihilation or extinction.

Here Paul speaks not of death in general but "the death", in a sense personifying it as a "king" over mankind from the Fall of Man until the giving of the Law at Mt. Sinai.

Reigned (936) (basileuo from basileús = a king) means to rule as a king, with implication of complete authority and right to control in an absolute manner. It speaks of the dominating quality of death.  This Death reigned as an absolute monarch over all unsaved humanity, exhibiting undisputed, rightful sway. In America, this picture might lose some of its impact. But to those who were raised in a country ruled by monarchy, the picture of a King whose decrees cannot be questioned is very real. So it was with "King Death".

Remember that in the beginning when man was created God looked and

"saw all that He had made, and behold, it was very good." (Ge 1:31)

It was very good also for Adam was not a sinner and there was perfect fellowship with God. But when Adam sinned all men became sinners and "the Sin" -- the sin principle or the sin nature -- came into the world through Adam and brought to fruition God's sure promise of death. And since death has indeed reigned in every man after Adam, it is empirical (originating in or based on observation or experience) proof that they were also sinners, having inherited the sin nature from Adam. They were sinners because they were all in Adam when he sinned and were thus made or constituted sinners (see note Romans 5:19).

So death is personified as a king reigning. Just as men could not defeat the rulership of "the Sin", similarly men could not usurp the power of death and thus they all died. Even believers die but there is a difference. Hebrews records..

Since then the children share in flesh and blood, He Himself likewise also partook of the same, that through death He might render powerless him who had the power of death, that is, the devil; and might deliver those who through fear of death were subject to slavery all their lives. (Heb 2:14-15)

In other words, yes believers die, but unlike unregenerate mankind, we no longer are in bondage to the fear that we will die and the certainty that death is the final hopeless chapter of their futile life. Not so with the believer for he is safe in the "ark" of Christ and will be delivered from the wrath to come. Paul echoed this triumphant cry for every believer of every age writing...

"O DEATH, WHERE IS YOUR VICTORY?
O DEATH, WHERE IS YOUR STING?"
(1Cor 15:55)

Thus even without the Law, death was universal. All men from Adam to Moses were subject to death, not because of their sinful acts against the Mosaic law (which they did not yet have), but because of their own inherited sinful nature and the fact that when Adam sinned, they sinned.

EVEN OVER THOSE WHO HAD NOT SINNED IN THE LIKENESS OF THE OFFENSE OF ADAM: kai epi tous me hamartesantas (AAPMPA) epi to homoiomati tes parabaseos adam os estin (3SPAI) tupos tou mellontos (PAPMSG):

Even - introduces a clause that shows there were no exceptions.

Sinned (264) (hamartano) means to miss the mark (and so not share in the prize) or to act contrary to the will and law of God.

Likeness (3667) (homoíoma from hómoios = similar) means resemblance or similitude (correspondence in kind or quality) so that they might did bread a direct command, written or verbal, but as Paul teachers, death still reigned over them because of Adam’s transgression.

The Amplified Version (I utilize it much like a "mini-commentary" - remember [brackets] signify clarifying words or comments not actually found in the original text and (parentheses) signify additional phrases of meaning reflecting the original words) helps understand this phrase writing...

even over those who did not themselves transgress [a positive command] as Adam did. (Erdmans) 

This same section in the New Living Translation (NLT) (which I also think can be a useful adjunct to your study if used with discretion realizing it is a paraphrase albeit in my opinion a relatively accurate paraphrase) (NLT - Tyndale House)

they all died anyway—even though they did not disobey an explicit commandment of God

Adam and Eve disobeyed a very explicit commandment. God spoke directly to Adam commanding him that...

from the tree of the knowledge of good and evil you shall not eat, for in the day that you eat from it you shall surely die." (Ge 2:17)

Because Adam and Eve were evicted from the Garden of Eden after they sinned, and prevented from returning, they had no more opportunity to disobey God’s explicit commandment. Neither they nor their offspring any longer had access to the tree of the knowledge of good and evil. Consequently, became impossible for any human being to sin in the likeness of the offense of Adam.

WHO IS A TYPE OF HIM WHO WAS TO COME: os estin (3SPAI) tupos tou mellontos. (PAPMSG) 

This final clause introduces the reader to the Adam-Christ typology, as a preparation for what is to follow in the next section.

Type (5179) (tupos from túpto = strike, smite with repeated strokes) (Click word study on tupos) means a "model" or "pattern" or "mold" into which clay or wax was pressed, that it might take the figure or exact shape of the mold. Type denotes the visible mark made by a striking some object (cf. "imprint of the nails" John 20:25), an impression made by an object that is in turn used to mould or shape something else (cf. "form" in Romans 6:17 [note]). Thus, Adam is an example of Christ. It is proper to speak of him as the First Adam and of Christ as the Last Adam (cf, 1 Cor. 15:45). It is interesting that the only Old Testament character to be called explicitly a type of Christ is Adam.

Hodge comments that in regard to the "religious meaning" type was...

a designed pre-representation or counterpart — either historically, as the Passover was a type or significant commemoration of the passing over, by the destroying angel, of the houses of the Hebrews in Egypt; or prophetically, as the sacrifices of the Old Testament were types of the great sacrifice of the Lamb of God. A type, therefore, in the religious meaning of the word, is not a mere historical parallel or incidental resemblance between persons or events but a designed resemblance — the one being intended to prefigure or to commemorate the other.

It is in this sense that Adam was the type of Christ. The similarity between them was not accidental. It was predetermined and entered into the whole plan of God. As Adam was the head and representative of his race, whose destiny depended on his conduct, so Christ is the head and representative of his people. As the sin of the one was the reason for our condemnation, so the righteousness of the other is the reason for our justification. This relation between Adam and the Messiah was recognized by the Jews, who called their expected deliverer “the last Adam,” as Paul also calls him in 1 Corinthians 15:45. (Hodge, Charles: Commentary on Romans. Ages Classic Commentaries or Logos)

And so the primary likeness of Adam to Jesus was that each was the head of their offspring. Christ is the head of all believers, even as Adam is the head of the human race. Adam and Christ were similar in that each one's single act affected their offspring. The first Adam affects his posterity for death, while the Last Adam gives eternal life to His offspring (not universalism but only to those who believe in Christ). Both Adam and Christ are one with their people and thus represent two unities, which are further explained in the following verses. This section serves as transition from the apostle’s discussion of the transference of Adam’s sin (Ro 5:12-14a) to the crediting of Christ’s righteousness (Romans 5:15ff).

Paul’s Jewish readers might have argued for their unique descent from Abraham the righteous, but Paul points them instead to their common descent with the Gentiles from the line of Adam the sinner. His argument would have greater force to his Jewish readers than Genesis alone might imply, because their traditions had made Adam much more prominent than he had been in the Old Testament (which is interesting because he is hardly mentioned outside Genesis). For example, Jewish people in this period sometimes spoke of Adam’s immense size (he filled the whole earth!), or more often of his glory, which he lost at the Fall. They believed that his sin introduced sin and thus death into the world, and that all his descendants shared in his guilt. Jewish interpreters generally believed that Adam’s glory would be restored to the righteous in the world to come.

To reiterate, the great truth of Ro 5.12-21 is that a representative acted, involving those connected with Adam and those connected with Christ.

Paul brings in the subject of death to establish the principle that one persons deeds can inexorably affect many other people. Paul’s primary objective in this chapter is to show how one Man’s death provided salvation for many, and to do so the apostle first shows the reasonableness of that truth since one man’s sin produced condemnation and death for many.

Wayne Barber summarizes Romans 5:14 stating that Paul is showing...

"the eternal effect of two people. One is a creation, the other is the Creator, Who became the God Man. That’s what we’ll see in the rest of chapter 5 as he says,