Application Manager
Slide over to the All column.
Scroll down to the Google Play Games app.
Tap on it.
Deselect the "Show notifications" option.
Different Android version may have different navigation and menu names
and groupings. I'm on 4.4.4 Kitkat.
I'm guessing "games" means the Google Play Games app. If you have other
gaming apps, you'll have to do the same to get to their "Show
notifications" option to disable it.
I've never used the Google Play Games app. I just tried but it halts
its use (which prevents me from looking at its settings) by first
demanding that I create a gamer ID. Since I'm not going to use it, I'm
not going to bother creating a gamer ID that I will never use. So the
above is how I would go about disabling ALL notifications by that app.
If you never intend to use the app, and because you are not allowed to
uninstall it (unless rooted), another choice would be to "Turn off" that
app. No point in wasting any memory or CPU cycles on a service or
background process that you will never use. Less memory used, less
resources used, less chance the smartphone will bog down. Actually, for
the Google Play Games app, once you select the "Turn off" option, it
then prompts if you want to uninstall it. Hmm, maybe you can uninstall
this app while not rooted. I didn't try to do the uninstall to see if
it really works (it's a new smartphone, my first, so I'm not yet ready
to be uninstalling anything other than what I installed since getting
back the pre-installed apps probably requires a reset which means losing
all the user-installed apps). For now, just disable its notifications,
then decide later whether or not you want to turn it off (which might
uninstall it).