What type of video games? That matters a lot to me. I can play a turn-based game like Civilization completely fine on little sleep (measuring the quality of play objectively, like by productivity or victory within a certain number of turns.) Soft real-time games like say a Mario platformer are a little worse but playable if I'm tired. Hard real-time games with very tight and sensitive timing like Guitar Hero or high-level Tetris are unplayable at anywhere near peak form if I'm not fully rested.