We could go around and around with this verse. Yes, on the day that Adam ate the fruit and sinned against God, God doomed Adam to die. I would argue that if he hadn't sinned, he would not have died.
But let me ask just a few questions, to help get us out of this loop:
1) Do you believe Adam and Eve would have died if they hadn't sinned?
2) How do you interpret Romans 5:15-21, which clearly states that "the many died by the trespass of the one man" and that "by the trespass of the one man, death reigned through that one man" and "sin reigned in death"?
3) And how do you interpret Romans 8:18-22, which speaks of a bondage to decay brought about by the Fall?
4) In light of Romans 6:23, would you say that death is *not* the consequence of sin? Yes, "spiritual" death, but also "physical" death. Death.
For what it's worth, I tend to reference the King James Version when making scriptural analysis, since that is the version I used during my formal studies. I find it helpful to share that info so whomever I am talking to doesn't have to guess. Hopefully I was correct in attributing your quote to the English Standard Version.
"We could go around and around with this verse. Yes, on the day that Adam ate the fruit and sinned against God, God doomed Adam to die."
The only reason we're going around and around is that you have no faith in God's word. You lionize your own instincts instead of trusting what God plainly says. That is hubris, not Christianity. The verse does not say God will doom him to death on that day; it says Adam will die on that day. You are simply wrong, and on some level you know that, because anyone who can read knows what that verse says.
"Do you believe Adam and Eve would have died if they hadn't sinned?"
They would have died physically, of course, but would not have suffered the spiritual death of separation from God.
"How do you interpret Romans 5:15-21, which clearly states that 'the many died by the trespass of the one man' and that 'by the trespass of the one man, death reigned through that one man' and 'sin reigned in death'?"
It means because of Adam's separation from God, his descendants, too, are separated from God (though they have the ability to get closer and closer through Christ). When it says "sin reigned in death," it again could not be talking about literal death, because simply dying is not a sin. Sins are things we do when we're alive. So for sin to reign in "death," we must be literally living, but spiritually separated from God.
"And how do you interpret Romans 8:18-22, which speaks of a bondage to decay brought about by the Fall?"
Same as above.