According to comprehensive rule 300.1 (page 56 of the linked pdf), the card types are: “artifact, conspiracy, creature, dungeon, enchantment, instant, land, phenomenon, plane, planeswalker, scheme, sorcery, tribal, and vanguard.”
Notably, battle is missing from that list. Probably just an error, but does this have implications for tournament play?
Can we think of any funny interactions because of this?
Some cards ask for a card “of a type not already chosen” or similar, so if Battle isn’t a card type, it wouldn’t be a valid target.
Others might ask for a nonartifact, nonland etc card, and Battles would be valid, as they should.
Worth noting as well, but even if you ignored the “Battle” type on the permanent, it is already possible and well within the bounds of the rules to have a permanent with no types (for example, mutate on top of a Theros god and lose the required devotion).