No, scrimmages don't count.
Lets say he has played 5 league games.
And lets say the minimum games at the moment is 7 games.
Then he will have to play 2 games in the same week so that he has played 7 league games, but then it will be the next week so the minimum will go up by 1 so now he will have to play another game to qualify.
Does that make sense?