Can Genymotion be used to play games?

Yes, but with limits. Genymotion can run many games, especially on ARM64 devices, but some games need Google Play Services, a non-rooted image, or features that are not emulated yet. See Can I play games with Genymotion? and I can't install or run an application/game in Genymotion SaaS.

For better chances, use Aurora Store when a game is missing from Google Play, and prefer ARM64 images. On Genymotion Desktop, many games work better on Mac M series than on PC or Mac Intel.