Horse is pretty enough.
Movement wise it's traveling hollow and pacing like a camel. Did not canter. Saw two slight "bobbles" in the backend. Could have been footing, but I'd carefully check stiffle action.
Horse seems well trained. Saw more "tail wringing" than I like but that might have been more an artifact of poor equitation than a physical issue. Still, it raises a "red flag" and means a careful pre-purchace evaluation (with or without a vet).
Price wise, you've a got $1500 horse with a $4000 asking price. Proceed accordingly.
The movement issue, assuming no physical issues, can be addressed by having the rider get their butt off the cantle and sit up straight. Then teach the horse to move more squarely using the "stair step" method. This can be done by an average owner and need not involve big bucks with a trainer. There probably should be a riding instructor/coach to help keep the rider "centered" as they work on centering the horse. In 90-120 days you could probably have this horse moving pretty squarely.