Being unable to install an app on your device from the Play Store is a pain. Fortunately, a developer has created a tool that lets you pull an APK directly from Google's servers and side-load it yourself. Handy!
The web app requires you to enter the package name for the app you want (which you can find in the URL of the app on the Play Store, after "id="), and after that it will generate a download link. The site only works for free apps — this isn't a piracy tool, after.
Remember, if you side-load an APK, you're taking the risk that it might not be properly supported. However, if you need to move an app over to a device without an internet connection, or you want to try it on a phone that's not officially supported, this is a way to do it.