A – If your asking for shabbat, we hold that games are muktse but of you must play there are some leniencies.
Lego is a machloket.
Backgammon and chess is fine if you don’t violate borer.
Puzzles, some allow if it doesn’t have a frame
Q – What does “must play” mean?
A – Must play might be if your kids very much need you playing with them or a person who’s a bit depressed and needs to ‘clear his mind’ etc.