To my eye he is much more of a sport pony type than a hunter type.
His neck ties on high to his shoulder in a way that is ideal for a dressage prospect, less so a hunter. He also has the uphill build usually associated with dressage horses, not the level build considered best for hunters.
As far as confo critique goes, he is long backed and is *very* post legged behind. He is also short/weak in the hind quarter, compared to the rest of him. Some of his difficulty with changes might be attributal to that, and it will be hard work getting him fit/strong enough to carry a good quality canter and improve the changes.
His shoulder is adequate to good, but doesn't carry the kind of angle that is associated with the flat, sweeping movement desirable in hunters. I also find it interesting that the ad shows him standing and jumping, but not moving.
To my eye, his head is out of proportion to the rest of him. That's a quibble that doesn't really affect function, but again, doesn't scream "hunter" to me.
Now, after I've been terribly hard on the cute guy, he does show good form over fences with an alert eager attitude that I like. You don't mention your price range or your daughter's plans, so if the price is right and your amibition is local hunter shows, he may be just the ticket.
But for reference, please compare his photo to some other ponies that are hunter types:
Now, those are some pretty fancy high dollar ponies pictured, and you're not going to find ones that look like them cheaply, but if you compare the overall proportions, the size of the head, the head and neck set, the length and back and the joint angles in the hind leg, I hope you'll see some of the points I made above.
ETA: Just watched the video. He's a better mover at the trot than I would have anticipated. Little more knee action than you want, but nice long stride with overtrack. The canter is what I expected, he has trouble maintaining a connected, balanced canter and the changes will be hard to fix.
His attitude and form over fences are pretty darn appealing.