Yeah similar to Sara my bf does it too but he also does his share. If your husband chooses to be tired fine, if he wants to complain a little about being overtired but still take care of things fine but if he is doing less bc of his choices then he needs to get it together. I've noticed it helps if you don't talk about why he was awake but the fact that he chose to be awake "I understand you're tired and I'm sorry about that but you chose to stay up last night". Never mention the gaming otherwise it becomes about "oh you don't like it when I play blah blah"
No he makes that choice of staying up and playing games but he’s still a father and that’s not a choice. He needs to man up an either stop staying up all night playing the game and find a suitable time during the day to do this or just deal with it because being a parent doesn’t end
My husband is the same way but I also play video games. He still wakes up regardless how tired he is to take our 5 year old to school. He’ll take over caring for our 2 month old if I’m too exhausted and/or taking a nap while he’s playing video games. Same goes with at night time as well as he’ll stay up late playing.