Steam says no licenses when I try to launch a game I own

Log out of Steam fully and back in, that clears it nine times out of ten, it's a stale license cache. If it comes back, check whether the game is actually in your library or being shared to you from someone else's, because if the owner starts playing anything you get bumped with exactly that message. Also worth a look at your purchase history in case it was refunded or revoked.