It's not meant to be taken literally as suggesting that the human is a dog themselves, but rather emphasizing the bond they share and how the dog might see them as a pack leader or family member.
Here are some examples of how the term might be used:
* "My dog human is away on a trip, so I'm being extra cuddly with my cat human."
* "The dog human finally got me a new chew toy! It's the best!"
* "I love my dog human, even if they do make me wear silly sweaters sometimes."
It's a fun and affectionate way to refer to the human in the relationship.