He’s going to play games whether he takes his own or has to find others to use theirs (or some schools have game rooms or allow them to be checked out).
I think I’d make an agreement for him to only play X number of hours per day/week and see how he does. Make sure he understands that staying in college requires him to make progress, have good grades, etc. You have to trust him.
My kids never played video games in high school but one started playing more in college. It was a social thing but it did become addictive. It is a time suck, that’s for sure.