After some back-and-forth with the developers (thank you all!) and some Internet research I finally resolved this problem. Versions of Android Studio starting at least in 3.3.0 are going to start complaining that the AppGameKit project has too many modules declared. You can try to fix this by enabling multidex (which for me, gave me something that compiled, but did not execute on a device) or by raising the minSDK level to 21 for the project as level 21 has built-in support for this issue.
The second problem I had after this is errors relating to the APK being split during installation, but this was solved by telling Android Studio to "Build->Clean Project" and "Build->Rebuild Project" (there may be a possibility you also have to "Generate Signed APK").
Goo Goo G\'Joob!