They control beasts and attack with them, that's why they are elite! You just don't see them listed, but the beasts are there fighting alongside the beastmasters.

Also, having beasts and beastmasters as military units would be too confusing. I accidentally trained strongarms instead of slingers, and they only have the first letter in common. Imagine how many would make the mistake of sending or training the wrong unit when they have the first 5 letters in common.

Magicians are cool, maybe you need to play more RPGs.