If you got good scores in an intro test, then the walk is probably ok. What you did show on the clip was a walk with nice clear, flat footed,4 beats - which is good. (ie no tension or jigging)
A dressage horse really needs to show overstep in all but the collected walk. without it, the scores for the walk(especially for med and extended walk) will not be good and this will also reflect in the collective marks. The walk can not really be improved in this regard.
I am not worried about the walk of the horse. It is fine. He looks very green and off balance under saddle, so I would not be making assumptions right now about limitations of his gaits, even the walk. He is not stretching right now, or balanced enough to reject his walk.
An overstep is not going to 'break' a dressage horse. This is a mistaken idea. The walk is judged on many things. Overstep is just one thing.
You did not show the horse jumping so I cannot tell if he is a good natural jumper.
I am surprised you say he could be more forward. Maybe the video just plays too fast, but the video does look like he is quick and somewhat off balance.
Right now he appears to be very green and a little confused. He is really quick from the video. You don't want any more forward you really need impulsion now than the forward. Even in the trot he is not tracking up that well but he does look very green. He could probably do both. I don't think he's got the movement for a A-AA winner but he'd probably have a piece of the hack. Depends on how competitve the circuits are around you. Work on his balance and getting him to use his hindend a little more. He's very cute.
Horses aren't our whole life, but makes our life whole
I would say he is definitely more of a dressage horse. He is not built like a hunter-- he has a higher point of shoulder, more dressage set neck, is not as horizontal or long as most fancy hunters. I think he will move more dressage like when he is going better. If he jumps well, he could be an eq horse in the future or a jumper (not high level) He could definitely do the hunters if he jumps well, but he is not a classic hunter type.