My boyfriend plays apex at 5 in the morning and I'm going to request that he stop.
Do you have a reason for wanting him to stop? Why does he play games at that hour?
I want to sleep. I stayed up with him until 2 am so many times.
At the end of the day, they are their own person, you cannot tell them what to do. If they wanted to come to bed then they would have. That said, he shouldn't expect you to stay up with him while he plays and he needs to keep the volume at a level that allows you to sleep.
Even if he wants me to stay up, I don't have to do what he wants.
You definitely shouldn't stay up if you don't want to, but at the same time you shouldn't tell him what to do if he want to stay up and play. Maturely explain your thoughts on the issue and perhaps ask him if he thinks he's getting enough sleep.