That’s not what I was asking!

[rivkat]

Help me name this trope: My favorite type of joke in the world has the following structure:

Peggy Noonan, stalling for time in answering a question and pointing to one of the portraits of luminaries lining the room in which she is debating: “Why is [noted conservative and killjoy] Bob Bork smiling down at us?”

Barney Frank, immediately: “Because it’s a painting and not a photograph.”

Funny because he's ignoring the meaning of the question, which is "why is there a picture of Bob Bork in this room?"

Or, in astolat’s Looking Glass Country:

“… I've had a good working relationship with Arthur [aka undersea king Aquaman] in my universe. I wouldn't mind re-establishing contact."

"Are you kidding me?" Clark said. "I don't have a good working relationship with—did you just call him Arthur?"

"Is his name different here?" Lex asked, and sipped his coffee.

Is it just a flouting of Grice’s Maxims, especially relevance?  Or is there some more specific name for the play on meaning at issue?