If I had a nickle for everytime I heard, “It’s arm wrestling, not leg wrestling?”, I'd be a millionaire!
However, I know for a fact that having strong legs will make you a better arm wrestler. It sounds crazy, but it’s true.
There is nothing worse for an arm wrestler than to have a huge masculine upper body and to have little chicken legs — a bad combination.
Arm wrestling uses every muscle in the body simultaneously and it is important to not only strengthen the upper body but also the lower body.
In my past competitions, I know that arm wrestling uses the legs and lower body; in fact, I have pulled my hamstring and calf muscles several times. For the record, that is not fun. This is the reason I push for full body workouts.

It took me several years to figure out that having strong legs makes you a better arm wrestler. I have always had naturally strong legs so this has not been a major limiting factor, but now I try to do regular leg exercise to keep them strong.
Having strong legs will make you a better arm wrestler. It sounds crazy, but it’s true. I like to dedicate one or possibly two days during the week to walk or jog or work the legs and the lower back.
Do what works for you but always try to include legs in your workout schedule.
I like to say that I am a good arm wrestler, but an even better leg wrestler :)