If you are compiling in Android, it should not be using the WindowsNetwork.h file at all.
The CoreForApp.h file is actually not used in the build, it is actually only used in the Tier 1 compiles. It just sort of got included in that directory at some point and has persisted.
If your Android build (in cygwin or using the batch file) is somehow including it, then your setup is not correct.
'cSpinLock' is defined in AndroidNetwork.h for the Android platform.
And, again, you don't do the compilation in Eclipse. You only 'run' it in Eclipse to create the apk from the stuff created by the cygwin build.
I just cleaned and built the template_android project, added it to my Eclipse, 'ran' it and it created the apk in the template_android/bin directory without a hitch.
I suspect that your Android setup isn't quite right.
Cheers,
Ancient Lady
AGK Community Tester and AppGameKit Master