Just like the new version of Google Play Movies & TV, the Google Play Games app sourced from the recent ADT-1 Android TV device update works fine on recent phones and tablets. There doesn't appear to be any huge functionality improvement in this release, it's merely a shiny new coat of paint. That being the case, it might be best to wait for the official phone/tablet update. If you don't want to wait that long, then have at it with the update below.
What's New?
Brand New Icon And Material Design User Interface
In addition to a swanky new icon, the interface for the entire app has been re-skinned with Material Design guidelines. There isn't much to say about it, except that it's quite pretty.
Strangely, the largest app icon in the APK's resources is 96x96.
New above, old below.
There are few small touches that are apparent: there's now a small link to your personal gamer profile on the Play Now page, and individual cards in the more detailed lists will show your achievements to the left instead of the right, as below. The "play" button has been removed, for some reason.
If you're worried about problems getting future updates, don't be: you should be able to uninstall these side-loaded APKs from the ADT-1, downgrade to the "factory" version of Google Play Games, and update via the Play Store when a conventional APK is posted. Unlike the Play Movies App, this one does not include "-tv" in the filename, so it may be the only version currently in development.
Download
The APK is signed by Google and upgrades your existing app. The cryptographic signature guarantees that the file is safe to install and was not tampered with in any way. Rather than wait for Google to push this download to your devices, which can take days, download and install it just like any other APK.
File name: com.google.android.play.games-2.1.10_(1477729-106)-21100106-minAPI17.apk
Version: 2.1.10 (compatible with Android 4.2+)
MD5: 23f395fe9873bc9c5aa2c8e8e4e339e3.
Thanks, Dave!