I looked quickly at your video. It’s not possible to give a definite answer based on a single movement but here is what I think.
Your left side (left on video as seen from the back) recruits your upper traps. This is typical of a shrug. Your right side does not or at least not as much.
This probably means your left side lacks some muscles and your trap has to compensate/take over. I would guess left lat given the movement your are performing. You can try to see that for yourself. Do a lats spread pose and observe if you see any difference in your muscles between left and right.
Now... why that is and how to fix it. Hard to say without discussion, history, further analysis. If my guess is right that your left lat is not as developed and is causing the issue : do some lats isolation exercises. And make sure you are using your lat and not shrugging. Otherwise you will only feed the issue.