Sometimes the claws splinter until they are really short especially if he's been climbing. An un-natural way for this to happen is when a cat is hit by a car & they try to 'hold' onto the road - short, ragged, bloodied claws are often the result.
He's biting them to tidy & clean them up. If you are worried have a look between the toes & at the skin at the claw base just to check there is no inflamation there that would indicate an irritation requiring vet visits.