No they don't. This challenge wasn't based on someone else having rights to the name, and nobody gets the "Redskins" trademark now that the team has lost it. No property (physical, intellectual, electronic, etc.) has changed hands, and this decision doesn't set precedent for that to happen in the future.

If the Apache group of tribes claimed that the word "Apache" was offensive, and managed to convince the USPTO that that was the case, maybe they could get the trademark rescinded, but that wouldn't mean they would get it for themselves, nor would it even mean the ASF would have to stop using the name, much less give up their website, only that they would no longer be able to sue other people for using it as well.

That's a different rationale, though. This trademark is being thrown out specifically because it is considered defamatory.

Even if the Apache Software Foundation were to lose the trademark on the right to exclusively use that word in the software industry, that does not mean they would necessarily need to give up the domain.

And bear in mind that trademark law does not aim to be a unique name registry. The trademark is issued in the context of the business. For example, the USPTO has trademarks registered for Apache helicopters and Apache skateboards, among others.