I haven't done it, but I would suggest you keep your login activities - which I presume you've used the xml layout for.
Your main game activity should use AndEngine and implement a BaseGameActivity
So your login screen would intend to launch the main game activity (that implements BaseGameActivity).
AndEngine does not have client/server stuff built in - just use the Android http communication functions
P.S. Instead of "CEO" you should call yourself Principal Software Developer. Unless you have an engineering degree, in which case you can call yourself Principal Software Engineer
"CEO" is all about money & direction of the company ... boring stuff