There is no answer (“Answer: 0”). If you got one it would be obvious because you would see the ip address. Either the DNS entry is not correct or your dig query does not work. I have not queried AAAA with dig myself yet and I am lazy on mobile. But you can try specifying manually using dig AAAA <your hostname> (at least that works with MX, TXT, CNAME and NS) records. (At least from the question section in your output it just says “A”, not sure.)
Edit: the output of dig is actually quite simple. Lines starting with ; are comments just four your information and improved formatting. Most you can ignore but some are helpful. Most important for you is stuff below your “Answer section” since everything below is, well, the answer for your query. If you do not have one (like in your example) the query did not return any results. This is also stated relatively at the top where it gives you a summary of the numer of queries, answers, authorities, … the request+response contained. There is also the question section (as a comment) which shows an A request, not AAAA. I think that shoud state the query you made which is not what you wanted. (Could be wrong though; never paid attention to that).
Well, uh, with Namecheap it should work just as fine as everywhere else. But as I said, I never used IPv6 and do not have anything on Namecheap anymore since I host my DNS server myself. Just a dumb question but are you sure you added the AAAA for the domain root correctly? Back when I used the web UI for DNS providers it was sometimes very confusing. Maybe you could test a subdomain? Like minecraft.yourdomain.com?
Also: you can query google.com if you want examples of how stuff looks when you get answers back.