Can't use Foursquare because it needs Google Play Services, which "is not supported by your device"
Google Play Services provides a "backbone" of sorts not just for Google apps but other apps as well. This is part of the way that Google is letting users and apps get to more "modern" Android features without having to wait for carriers to update their version of the OS.

I'm guessing that the phone you're using didn't come with Google apps installed.

See if you can install Google Play Services directly. 

If so, you should be good to go.

If not, you're probably out of luck.