A friend's daughter had restless leg syndrome, which this sounds like except that his arms are also involved. Which is probably why the term periodic limb movement came about. There's a children's nutritional product which helps restore balance to the body - couldn't hurt, might help this, will certainly help overall wellbeing. If you want to talk to her, I can connect you.
You'd be surprised what can turn up in a sleep study. There can be small movements, slight breathing interruptions, and/or brain activity that can be recorded whether or not there's visible movement. It also can determine when in the sleep pattern this is occurring, which is actually useful information. I had 2 studies and was astounded at what they came up with.
Depends on whether you think this is urgent or not. No harm in getting the sleep study done if your insurance covers it.
But I don't think you should panic over possible seizures - it's really impossible for us to diagnose it from our vantage point. A cell phone video might be okay - it will record the movements although not necessarily give definitive clues about the cause.