I just installed it on my Vizio tab with out an issue so I don't know what it could be but here are some ideas have you tried rebooting your device and you might need to clear the data for the play store.
I am having the same problem. Galaxy S2. I have tried absolutely everything. I've uninstalled and re-installed several times, cleared cache, force stop, reboot, taken battery out. My case is really weird, however. The app itself is on my phone I can run it perfectly fine and it plays music perfectly fine. However, it will not sync with my HTC playlists, first of all. Second it will not register as installed under "my apps" in Google Play Store, but it does show up under settings, applications, manage applications. I'm dumbfounded, perplexed even. Is anybody else having any problem even remotely close to this???