Maybe a little, but there’s more to fighting bullies than hand-eye coordination.
I was able to fight bullies when I was about 5, before I’d even seen a video game.
My impression is that attitude and taking action is the main thing that works in fighting bullies. Often, bullies are bullying because they are afraid, and are not actually prepared to fight, so someone actually attacking them will often get them to stop.
When a couple of times, much later, I found my car losing traction and spinning out, I was able to react and avoid crashing, and I had the impression that my video game experience may have helped me react effectively. However, I have no self with no video game experience to compare to, so I don’t know.