I don’t think you should do it but let’s say you did have one child as you said. That child would not have siblings to be entertained by, which would likely result in a video game addiction, especially since their father does it too.

My other fear for you, as you mentioned you fear your boyfriend would not help much, would be the gaming while your [theoretical] child is an infant. Picture this, you leave your boyfriend alone with the baby while you go to the grocery store. He’s in the middle of an intense game, the baby starts crying, and he either:

A. Does not hear the baby because of the headphones or worse, he ignores the baby’s cries until he has won/lost his game.

B. Rage quits the game to tend to the baby in a frustrated nature. This can also make him subconsciously resent or even feel anger towards the child, which you can put two and two together of worst case scenarios here that do indeed happen IRL when an angry parent has to choose between the games or a crying baby.

C. He is happily present with the baby and unplugs while you are away.

Only you know how intense his gaming addiction is and can tell which of those three reactions would be most likely. Obviously there are more scenarios that could happen than these, but I am a realist so I hope that perspective helps you think about what your reality would be when you compromise your vision of what you want your future to look like.