Play games on your Mac
When you sign in to your Game Center account on your Mac, you can play single-player and multiplayer games (both real-time and turn-based).
Apple Support
You can connect a game controller with your Mac to play games. See the Apple Support article Connect a wireless game controller to your Apple device.

If your game controller supports it, you can specify actions to occur on your Mac—for example, open the Games folder in Launchpad, take a screenshot, or record a brief video of gameplay—when you press designated buttons on the game controller. To set these options when your game controller is connected to your Mac, choose Apple menu > System Settings, then click Game Controller in the sidebar. (You may need to scroll down.)

Open Game Controller settings for me

Games you download from the App Store are added to the Games folder in Launchpad. To open a game and start playing on your Mac, do one of the following:

Click the Launchpad icon in the Dock, click the Games folder, then open the game you want to play.

If you’re using a Bluetooth game controller that supports it, press the designated button on the game controller to open the Games folder, then open the game you want to play.

If you don’t play a game anymore, you can easily remove it from Launchpad.

Note: Compatible hardware and software are required to play some games.

Let a game find other players: If the game provides Auto-match, click Play Now to let the game find other players for you.

Play nearby players: If the game detects nearby players who are on the same Wi-Fi network as you, or within Bluetooth range, it shows them. In the game, select a player.

Invite friends to play: In the game, click Invite Friends, then select people from your contacts, friends, or nearby players. Customize your invitation, if you want, then click Send. You can send your invitation as a message, or send it to a phone number using SMS.

Accept an invitation: In the notification or message, click Accept. The game opens (if you have it) so you can start playing. If you don’t have the game, the App Store opens so you can get the game.

Record a brief video or take a screenshot while playing: When you use a Bluetooth game controller that supports it, press and hold the game controller button you specified to use for recording or taking a screenshot. You can record up to 15 seconds of gameplay.

Make sure Game Center notifications are turned on in Notifications settings, so you know when you’re invited to join a game or that it’s your turn to play. You can receive Game Center notifications even when you’re using a Focus. See Set up a Focus.