The guy is just very backwards on the characters...I get it's a joke, and not to take it too seriously, but, what it actually is:

Batman: He's called Batman because he dresses like a bat in order to instill fear into the criminal underworld of Gotham...he came up with it, because he himself was afraid of Bat's, and that is the reason.

He is expressly not an adrenaline junkie, and does nothing without a ton of research and prep time; and his gadgets are not for fun, they're all for specific purposes of taking down bad guys while limiting danger to him, them, and the public.

He's actually a depressive recluse, that only fights crime due to having severe mental health issues after his parents were killed in front of him.

Daredevil:

He doesn't have this name in reference to his ability to fight crime; but from the fact that he fights crime in the Hell's Kitchen neighborhood of New York City...while he was doing that, the Hell part went along with Devil nicely, and he was named that by the press.

If anything, he is the adrenaline junkie. Though he has a rough past himself, he constantly tries to leave the crimefighting life for one reason or another and is dragged because in because his character just needs to be a part of the fight...His style is also much more random and "daredevil" like, because he essentially just stands outside, waits to hear some crime, and then jumps off the side of a building using a grappling hook toward it, without any preparation.

So their names actually do make sense, and the joke really doesn't, if we're actually breaking it down.