I have never had experience with something like this and I am quite interested to hear other members responses. However, I would get a dentist out - each horse would be different, each case would be different.
Your horse is not in any danger at all with missing teeth. As long as he/she is eating and maintaining good body condition there is no need to fret over missing teeth.
However, you may have just discovered the interdental space of your horse's mouth. Every horse in this World has an upper and lower interdental space in their mouths, also known as the "bars". This interdental space is where when bridled with a bit the bit rests on the tongue when no pressure is applied. Then upon using the rein pressure is applied to the tongue and roof of the mouth.
It looks to me like maybe we got kicked in the mouth by another horse or some other injury. My friend in CA has my old Morgan, Pepper and his front teeth look similar but more teeth missing. He had a bad fall in the arena a few years ago and landed on his face and knocked them all out.
As long as the back teeth are still fine (you should have a vet check for you) I wouldn't worry. The front teeth are fore pulling grass, biting off food. As long as your horse has plenty of hay etc available so that he doesn't have to use front teeth, I wouldn't necessarily worry about it. Pepper does fine on hay and his grains are mixed with water or molasses to make them stickier and easier to eat.
I'm having a hard time with the photo so I'm not positive what the gums look like, but my old guy. I took him in to get a root canal and the vet said "Let me check to see how loose this tooth is before we get into a root canal" and he jiggled it, the tooth came right out, no blood even. The roots had completely died and gone away....