He looks all Arab to me as well, and may have some Egyptian in him. LOTS of reasons not to register a purebred, the biggest being if they're geldings and not halter show quality, it's an expense that doesn't really add value.
The Arabian breeder I worked with not only didn't register the less than top quality colts destined to be geldings, they gave a lot of them away, and that's when the market was much better than it is now.
I'm sure you'd love to know his pedigree, but other than that, unless you planned to show him on the Arabian show circuit, would papers really matter?
He looks like a delightful, useful, all around good guy - I wouldn't care if he was 1/4 Bashkir Curly! Hope you have many years of enjoyment with him.