How can I turn off the gamed service or more generally, any service?
Specifically for the gamed service, the following command in one of the posts about a similar topic on the Apple Support Communities worked for me, without any need to modify plists or rename files:

sudo defaults write /System/Library/LaunchAgents/com.apple.gamed disabled -bool true


Changing "true" back to "false" will re-enable it, although I've not tried it.