Part of macOS
gamedGames
○ Leave it
Runs Game Center, Game Mode and game controllers.
What it is
Handles Game Center, Game Mode (which gives a full-screen game priority) and controllers.
If you stop it
macOS starts it again straight away. Leave it.
The verdict
○ Leave it. Part of macOS, or something that starts again by itself. You never need to close these.
In Activity Monitor
gamedgamepolicydGamePolicyAgentgamecontrollerdgamecontrolleragentdgamesaved
From Procession’s guide, in the words the app shows.