So what do you think it means that they "had not sinned after the similitude of Adam's transgression? Adam's transgression was that he disobeyed a direct command from God. That is God spoke to him directly and gave him a command not to eat of the tree of good and evil. He disobeyed. Those that had not sinned in that same way also sinned, just not in that same way. They had no direct commands from God. However, earlier in chapter 2, Paul spoke of the others, the Gentiles, that "when they, who do not have the law, by nature do what the law requires, they are a law to themselves, even though they do not have the law. They show that the work of the law is written on their hearts, while their conscience also bears witness, and their conflicting thoughts accuse or even excuse them on that day when, according to my gospel, God judges the secrets of men by Christ Jesus (vv. 14-16) Therefore, they didn't sin in the same way that Adam did, but they did sin. And judgement was/is meted out accordingly. So yes the died, but the died spiritually due to the sin. They did not die physically (biologically) due to sin. And so, as Paul says in verse 14 of chapter 5 that "sin indeed was in the world before the law was given", They sinned, they died spiritually.
Interestingly, Paul adds there, that "however sin is not counted where there is no law". But as I have noted, in chapter 2 Paul has already stated that there is always law, just not the law of Moses. So what can he possibly mean by that. I firmly believe that he is talking about the very young and those so mentally deficient they cannot understand and comprehend the consequences of either obedience or disobedience. The very young and the mentally deficient cannot and do not sin.