All I did was turn on my bluetooth on my phone, turn on moga pro controller (on HID - orange) and run FPse. After loading a game (Gran Turismo) I've got a message on the screen saying gamepad detected and it worked just fine. Then I turned on Vigilante 8 2nd Offense and noticed that the L2 and R2 buttons aren't working and I tried going into settings and mapping it but the app doesn't seem to recognize those two buttons. And I did not try the Bluez IME but thank you for suggestion.
P.S. I only have moga pivot app installed.
edit: From Bluez IME app description: "Reported NOT working with any LG device with stock ROM:" and I'm running it on LG Nexus 4 with stock so no help there
Also, I've tried ePSXe and I've got the same issue involving L2 and R2 buttons not working (the app isn't as intuitive as FPse and you have to map all the buttons and edit control settings). I know those two buttons work and controller isn't defective because I've tested them on MOGA Pro supported games such as Shadowgun and Modern Combat 4.