Per the FAQ:

Q: Why is this web site reachable via IPv4 only?

You're right, there are no AAAA records, intentionally. A percentage of users are unable to browse sites that are dual-stack. If the users can't connect, then they can't be told they have a problem. This is a big problem facing content providers today; of which, I work at one for my $dayjob. As such, the main test page requires IPv4 (either native or translated).

At some point, when the percentage of "broken" users has gone significantly down, I'll consider making test-ipv6.com dual-stack..