Can there be a sarcastic meaning to "top gun" in a (non-)linguistic context like this?

In a speaking practice recording, a guy (Person A) is trying to place himself at the center of attention in a conversation about his job. The conversation goes:

Lady: Veronica talks about you all the time. I guess you must be pretty busy at work.

PERSON A: Well, yeah, a V. P. position is not easy, you know! I implement policies and procedures nationwide, of various departments, as well as train junior managers in FDA and EPA regulations. [...] that alone means I have 1500 employees under me. [...] what do YOU do for a living, Arthur?

Arthur: Oh, I'm a TOP GUN PILOT.

I can not see exactly how this response could work against a guy who is going on about his fabulous position at work.

Solution 1:

Arthur is claiming (probably falsely) to be a top military pilot in reference to the old Tom Cruise movie Top Gun. He is attempting a put-down of Person A by making himself out to be more 'manly' than the V.P.

It is also possible that he is using an obviously false claim to military prowess and daring to imply that Person A is exaggerating his importance.

Solution 2:

"Top gun" is used as an informal expression to refer to;

(Slang) a person who is the best or one of the best in a particular field; the top-ranked person in a group.

Dictionary.com

In your conversation Arthur is using the expression "top gun pilot" ironically to contrast Person A description of their job which apparently requires top skills.