X.Org Might Lose Its Domain Name

They're not losing it because of some legal battle or copyright claim, they're losing it because they lost contact with the guy who really owns it, and waited until they had one week to go to make the issue public.

A project that loses an asset that valuable, because they cannot get their act together until one week before the disaster is going to die sooner or later anyway, even if you disregard that they are indeed already dying.

Couldn't they file a trademark claim to takeover ownership?

What a terrible lack of information in this article.

No, they're in danger of massive registration headaches because they don't have a clear chain of proof of migration from the LLC (since dissolved) to the 501(c)3 that succeeded it, and they're either not in contact with the person who was the administrative contact when the LLC existed or he's being unhelpful. I'll note that the listing was last updated in 2007, so his name's been on the contact info for 8+ years - probably at that time they renewed for as long as the system would allow.

There are provisions in place for replacing contacts on registered domains when the contact is someone no longer with an organization, and I'm pretty sure those aren't generally all that onerous (since incorrect changes can be reverted) - generally something on organization letterhead, probably a drivers' license photo, that kind of thing. In this case because the originally registering organization no longer exists they basically need proof that either the current foundation is legally the successor entity or they need proof that the domain name was part of the "assets" transferred to the new 501(c)3. They could probably have just sent in a change request on the current letterhead, but I suspect that A) they're no longer at that address either, B) Someone at Verisign said "Hey.... If we force an expiration we can auction this sucker for $$$$$$", or C) Leon Shiman could be expected to object to a change.

Another problem is the question of whether there's a registered trademark for X.Org - if they had that, even if someone else snagged the domain I suspect they'd be able to get it back via UDRP. Unfortunately it's not clear from a quick search that it's ever been trademarked, which likely drastically complicates the situation.