Looked at the FAQ but could still use some suggestions as the list is not thorough (Esenthel being one of the engines that seems to do Android but is not on there).
Correct. That looks like a fairly minor engine.
* Ability to code for Android in C or C++
* API to get user's location
* Send and receive data to/from a server (it would need to store small bits of information, like said location)
The first requirement you can do with just about any Android engine that lets you write platform-specific code; it isn't difficult to add native code to a project, especially when you have the source of the engine. If you want an engine with the core functionality written in C or C++, there are a few of those. I'm assuming Cocos2d-x doesn't meet your needs because you want other features, but it might do what you need.
The second requirement is something you get with Android automatically. It all exists in a nice little bundle inside the com.google.android.gms.location package. If you want to access it in C or C++ code you'll need to wrap it up yourself, or just use the Java package.
Network communication is common in game engines, and many people have written stand-alone libraries with game-centric functionality. Shouldn't be hard to find something that meets your needs.
I don't know of any Android-specific game engines that specifically use both the first and second entries together, you'll probably either need to wrap the gms.location interfaces you need for your app or just switch to Java.