I believe that that saddle pictured is a close contact saddle.
It is not a dressage saddle, because their flaps are not curved and dressage saddles have a very deep seat. All-Purpose saddles have a slightly more shallow seat than the Dressage, and curved flaps with bigger knee pads than the close contact saddle, padded panels, and most of the time a round cantle.
Close contact saddles have a relatively flat seat, like saddle seats, squared cantles most of the time, forward flaps with minimal knee pads, and thin panels to feel the horse's sides.
Close contact jumping saddle:
All purpose saddle:
In my humble opinion, if you prefer for the horse to feel you go with the close contact, because your horse will be able to feel your legs much more easily than in any other saddle. But honestly, you could really go with any saddle, if they are used to you being on their back, there should not be much trouble with a saddle on their back. If anything plop the saddle on, and lunge them, and add some weight to the stirrups to get him used to the feel of the saddle. : )
Has he been ridden with a saddle before, or are you just breaking him in?