Bare knuckle boxing requires training, you can't just throw a normal boxer into the ring and expect them to adapt; because they won't.
Punching someone in the head without gloves will break your hand, so it's not something you can do a lot, so bare knuckle boxers practice giving and taking more body shots. They also condition their hands like other martial artists. But a boxer used to fighting with gloves is trained to protect their head and just take the body shots, which will break ribs without the padding and they'll break their hand with the first or second head shot.
So the fight that was shown was very obviously choreographed, and no-one involved knows about bare knuckle boxing.