Rules vary a bit, from what have seen. One school suggests this:
# Only bows that are not center shot and without any aids may be used in competition. Only a nocking point is allowed. Examples of aids: handle or grip locator, sight window, arrow rest, stabilizer, or marking construction etc. The bow can be made of synthetic or natural materials and the draw weight is not limited.
* some allowable examples: bows of the horseback archery peoples: Scythian, Hunnish, Avar, Hungarian, Mongolian, Turkish etc.
* Asian-style bows, Chinese, Korean, and Japanese.
* European stick bows, longbows, etc.
* Bows of the peoples of North and South America.
That's Kassai, who is basically horsearchery Marmite.
The Kaya bow may not be allowed by the Kassai school, but then they basically disapprove of anything that isn't a Kassai bow. You'll be fine in this country, at EOCHA (European Open) and the World Championships. At this year's EOCHA, the Koreans were using Kaya bows (or very similar) and a Turkish archer I know uses one as well.
I have to say that I'm not convinced of the efficacy of an arrow shelf for horseback archery. It's awfully bumpy out there and you're trying to nock very quickly. It's not uncommon to have the arrow bounce off your hand, and I'm sure it'll bounce off an arrow shelf.