In common parlance, we say "s/he pretends s/he doesn't understand", for people who ignore the context of the conversation and require hyper-specific definitions to keep the conversation going.
(hyper-simplified) example of the above, in the form of a dialogue:
Q: Hey, how's your day?
A: In what sense?
Q: Uh, let's say for the sake of argument, how's work?
A: What do you mean by that? In terms of what?
Q: What are you up to?
A: I do lot's of stuff, you have to be more specific - is there something in particular you're interested in?
Q: Nope just in general, are you enjoying it?
A: Sorry I don't understand, define "enjoying it" in the context of work
and so on...
Is there a term for what the person (A) is doing?