Translation:Do they enjoy playing games?
Yes, that is the more natural way, but VV 不 VV is also correct. https://resources.allsetlearning.com/chinese/grammar/Affirmative-negative_question#Verb-Not-Verb
Isn't 玩游戏 a bit redundant and awkward? I've always thought 游 means play and 戏 means games, and 游戏 can also be a noun that means games (e.g. 这不是游戏 - this is not a game). Also, 玩 means to play in general or it can be followed by a very specific noun indicating what is being played.
I don't think this is redundant or awkward. 游戏 is a fossilized compound that means "games" and can't really be broken down into its constituent parts. The character 游 now usually means to travel or to swim and 戏 usually refers to theatrical plays. The closest I can come up with right now in English would be something like "pulling a drawstring" where "to draw" is sorta synonymous with "to pull" – not awkward or redundant.
玩 is "play". you can play in a yard (在院子裡玩), play a ball (玩球), play a video game (玩電動遊戲), play a cardboard game (玩紙板遊戲), play hide and seek (玩捉迷藏), play music (玩音樂), etc.
打 is "hit". hit a person (打人), play a drum (打鼓), etc. you can also say 打籃球 (play basket ball - because you really hit the ball) too. Some video games are "hit" something, so you can say "打遊戲".