From Sega Retro
I've corrected the speculation that the third button on this joystick functions as the other two combined. Unfortunately it does not.
Having tested this with the Mega Drive, I believe this joystick was designed primarily for that console and secondarily for the 8-bit consoles. Its function is consistent with other MD controllers when used with the Master System -- the A button is nonfunctional.
One further confirmation - the box for the XE-1 ST2 says Mega Drive in Japanese.