I hate the Shield. I didn't want to play games on it, I play like one android game and it runs on my phone just fine. I just didn't do any research, and bought that thing with the best hardware that everyone was recommending and it's the purchase I regret making most in recent memory. I hate the Shield's Play store, and the inability to install basically any app I might ever want to use. Is there any box out there with decent hardware, not very buggy, which has a more default Play store version, more like the one you'd get on, say, a tablet?
The the play store on the Shield is the full Android TV Google Play Store. The only reason you don't see "all" the apps you're used to seeing is the fact that the developers have to list their app's compatibility with ATV. There's usually a good reason (at least to the developer) for the app not to be listed that way if it's not already showing up.
You can often sideload the app (if it's free) from someplace like APKMirror . If it runs, it runs. If not, oh well....
If you rooted the Shield and and edited the build.prop file to say you were not a Shield TV (running ATV), you could theoretically see the whole GPS for the version of Android you're running, but that's not for the "faint of heart".