There are many version with different answers to "what it is a Tengu", but as far as I know, the most common version is that Tengus are beings advanced enough in the Buddhist arts to gain Buddhist magic power, but who never reached enlightenment because that involves ridding yourself of your personality flaws, and this person has one specific flaw they're so proud of that they don't want to let go of even if it comes at the cost of never becoming enlightened. Their inhuman traits are result of the Buddhist magic power in their bodies being corrupted by the flaw they attached themselves to.
If you think about it, Pepe has a very decent chance of turning Tengu in his next appearance, assuming he isn't already one.