Why is it important to understand that the verb "marry" carries this slightly different meaning?
It appears that you are using "slightly" facetiously. Please correct me if I'm wrong.
I think that the understanding of the Greek word "gameō" as meaning "sexual intercourse" is important in understanding our Lord's teaching.
Many think our Lord taught that if one divorces his spouse and marries another, he is committing adultery against his spouse. But would that be the case if his spouse is no longer married to him? They teach also that if one divorces his spouse, he is causing that person to commit adultery against him, and the one who marries a divorced person is committing adultery against her husband.
Even the translations support this position. For example:
And he said to them, "Whoever divorces his wife and marries another, commits adultery against her; and if she divorces her husband and marries another, she commits adultery." [Mark 10:11-12 RSV]
"But I say to you that whoever divorces his wife for any reason except sexual immorality causes her to commit adultery; and whoever marries a woman who is divorced commits adultery. [Matthew 5:32 NKJV]
But how can a man who divorces his wife and marries another commit adultery against her? He is no longer married to her. How does a man who has divorced his wife cause her to commit adultery against him? She is no longer married to him. How does a man who marries a divorced woman commit adultery against her former husband? She is no longer married to him.
The apostle Paul, who was very familiar with this teaching of Christ, does not seem to have understood our Lord in this way. For he wrote:
Have you been bound to a wife? Do not seek to be loosed. Have you been loosed from a wife? Do not seek a wife. 1 Corinthians 7:27
Paul seemed to teach that one should remain in the state he is in.
I understand Paul's words about having been bound to a woman ["woman" and "wife" are the same word in Greek] as having made a mutual commitment with a woman for life. He should not seek to be loosed, which I understand as not seeking to be divorced from her. But is he
has been divorced, he should not seek a wife.
But notice the next verse!
But even if you do marry, you have not sinned...
If he has been divorced from a woman, and marries someone else, he has not sinned! But if the translation of our Lord's words is correct, he
has sinned! He has committed adultery against the woman with whom he had been married.
Again, Paul was well-acquainted with the teachings of Jesus. He would never have taught the negation of our Lord's words.
Let me translate the record of our Lord's words in what I believe to be the correct way:
]And he said to them, "Whoever sends away his wife and copulates with another, commits adultery against her; and if she sends away her husband and copulates with another, she commits adultery." [Mark 10:11-12 RSV]
If a man easily dismisses his wife [or as we would say today "separates from her"] and takes up with another woman, he commits adultery against his wife. He is still married to her.
Jesus said this in the context of having been asked further about His words:
"What therefore God has joined together, let no person separate."
And the other passage:
But I tell you that every one who sends away his wife, except on the ground of prostitution, makes her an adulteress; and whoever copulates with a dismissed woman commits adultery.
Again, Jesus is speaking about a person who easily dismisses his wife. He makes her an adulteress against him, if she takes up with another man.
Any man who copulates with a woman who has been dismissed by her husband commits adultery against that husband.