If he's been 4 since 2012, then jumping isn't a problem. A horse can start jumping at four because that's the average age most horses' knees lock into place. My vet, who is also my former trainer, liked to keep horses jumping from 18"-2'3" their first year, depending on the horse. She didn't jump them more than twice a week and only upped the workload during their five year old year. If this video is of this horse late into its fourth year, I don't see a problem. However, if it's been jumping since it was a three year old, then there could be some serious issues with arthitis later on.
Regardless, a vet check is ALWAYS a must if its an unfamiliar horse and barn.