jackiabu, I watched your video...twice. I'd like to try and help.
I believe the problem is that your gun is NOT calibrated correctly with your computer. That's why the cursor jumps all over the place on your monitor. Forget MAME for now. You need to get the gun(s) calibrated.
BadMouth's comments and input is good.
My AimTrak's are slightly different (Arcade Guns). I'm not sure which gun trigger is your calibration button. For me it's the large rear button. Where your thumb touches. I have to keep it pressed down for at least 10 seconds uninterrupted for the lightgun to enter calibration mode with Windows. Your gun may require more or less time. 5 seconds? Maybe I missed it in the video but it didn't seem like you actually entered calibration mode. Hard to see. Somehow you may not be pushing the correct button long enough...or something.
You will know you've entered calibration mode when the mouse cursor moves to the upper left corner of the screen. At that point, release the large button pressed to initiate calibration. As BadMouth suggested, don't point your gun at the screen when initiating calibration (pressing the large button on the gun).
Now...once the mouse cursor is in the top left corner, point the gun at the mouse cursor (using the tips I posted prior) and pull the trigger. Do the same for the upper right and bottom center. The center target will be slightly off center. That's OK. It's supposed to be so. You must aim VERY carefully at these three targets. Take your time. Use the iron sights of the gun.
If your calibration was accepted you should be able to control your mouse cursor with the light gun. You should have smooth cursor control across the whole monitor. If you like the accuracy of the gun then you're done. If not, re-calibrate until you are satisfied.
If you calibration was not accepted by the software (actually firmware), the cursor will return again to the upper left corner of the screen for re-calibration. If this happens, don't be alarmed. Move a foot or two further away from the screen and try again. If you are already more than 7 feet from the screen you should move closer to the screen instead of further away from it.
If accuracy is still not quite right after calibrating, start the calibration process again. This time you might try aiming slightly above or below the mouse cursor target or tipping the nose of the gun upward or downward during calibration. Again, I still suggest keeping your wrist and arm as motionless as possible.
I know this can be frustrating.

I remember having to try to calibrate my guns many times before I got it right.
The good news is that once you get them calibrated in Windows you won't have to worry about it again. The calibration for you screen stays in firmware. Even if you unplug your guns.
Then...you can move onto MAME.