What is the legal age to run a site?

[ZiNgA BuRgA]

I don't think there's any issue with MyBB and underage dealings.
All in seriousness, do you expect parents to watch over their teen kids like a hawk?

As for legalities, I don't think people should care that much, though it seems that the MyBB community is far too serious on that side.  Seriously, it's a community project and people should just get along with each other, not think of ways to trip other people up.
And whether something is legally binding doesn't mean much.  If I go steal a paid plugin and use it on my forum, what can the other party do about it?  If a C&D doesn't work, what options do they have?  Apart from some form of defamation perhaps, it's seriously not worth actually pursuing legal action against me.  If they did, at best, they could only reclaim damages (the $5 or so they didn't get), and that's about it.

I think people should generally stop thinking about legalities.  Law on the internet is rather dodgy at best, and in many cases, never enforced.