The letter you received (which was nice of them to send!) is letting you know that your use may fall under "fair use" as set forth in US copyright law
Section 107 contains a list of the various purposes for which the reproduction of a particular work may be considered fair, such as criticism, comment, news reporting, teaching, scholarship, and research.
If you're making a game, then none of those would apply. They don't know if your use would fall under 'fair use' because 1) as they say they dont' give legal advice and 2) as they mentioned, they didn't review your submission (because the don't have adequate staffing to review submissions).
My hunch is the letter you received is a standard lawyer-approved response to anyone who writes in unsolicited asking to use Nintendo properties.