Okay so now I am even more confused with what is going on...
I was messing around with MAME.ini and I got a clean groovyMAME one and compared them and made a couple changes, and still nothing.
I did try setting the deadzone value up higher, and set it to 0.5, and I definitely noticed a difference with tracking in the center of the screen, so I know it's reading that value from MAME.ini.
Then under the CORE INPUT AUTOMATIC ENABLE OPTIONS section I had both the lightgun_device and positional_device set to "joystick" which the USB2GUN is recognized as.
So I removed it from positional_device and no changes.
Then for shits and giggles I decided to remove it from lightgun_device as well, so that I had no devices set to "joystick", and loaded up MAME.
And to my surprised, I am STILL getting the same exact behavior. It's still recognizing the happ gun for tracking even though I do not have joystick set anywhere in MAME.ini which is completely baffling to me. I also checked it inside MAME itself and nothing was set to joystick either.
I did notice that mouse_device was set to "mouse" still so I wonder if for some reason, MAME (or maybe the PC) is seeing the Happ guns also as a mouse input device?
I am going to see if I can play around with this more later on too, but if anyone has any ideas, I'm all ears.