How do I get my Arduino Mega 2560 registered as a game controller?
You would need to either:


Change the firmware of the USB interface chip on the Mega2560 to act as an HID game controller.  There's a second ISP connector for that purpose.
Run a software USB emulation on the main ATMEGA cpu and have that be a game controller.  You would need an additional USB connector and supporting passives to approximate the electrical interface.
Add some additional USB interface
Write a driver for the host operating system that accepts input over CDC USB serial and injects it into the operating system as if it were from an HID game controller
Modify the client programs to take serial data instead