Okay... I have the same X-Arcade that you do.
Keep in mind that the X-Arcade is basically a "keyboard" and the trackball is a "mouse". If you plug the X-arcade into a PC and open something like Word and press buttons it will put letters etc in WORD.
I looked at the specs for what you bought and as usual on almost all this Chinese junk I am scratching my head.....
There is this image -
It looks like you can connect external USB joysticks. I am not sure if they just act as player 3-4. But this is not even a picture of what you bought. (Even though it is in the same listing.)
Here is what I would do -
#1 See if a PS2 controller works.
If a PS2 controller works then go buy this -
If a PS2 controller doesn't work then I am not sure what controllers will work (if any). There are adapters for quite a few controllers.
With all that said.... Launchbox/Bigbox setup on an external HD is really the way to go. I just grabbed a Western digital WD-BLACK 5tb HD for like $100 and will be setting up a sweet retro system that I can plug into any computer and play greats games with amazing emulation. BigBox will cost you $60 (not needed, but worth every damn penny.).
So for about $160 you can turn any PC into a retro gaming system that you can use on any PC and take on the go.