I’m kind of disappointed about this penalty game, but I’m also a little excited.
A penalty game (ゲーム) is a fun kind of game you see on Japanese television a lot. When you mess up, you are punished. Usually it hurts. You can call this a batsu game or a penalty game. Don't call it anything else, though, or you know what happens...
This is a jukugo word, which usually means on'yomi readings from the kanji. If you know the readings of your kanji you'll know how to read this as well.