Not legal advice, but I believe denying all facts even the ones that are obviously true is setting himself up to pay costs for proving those facts, even if he was to win overall.
Nintendo are over litigious and have a reputation for weaponising copyright laws to shut down legitimate competition - but I suspect this might not be a good test case for challenging this.
No point asking them to justify why they have to ask, they probably don’t even know. Just say “Sorry, I don’t give that out”. I’ve never had a store push back after that - they probably get it all the time.