Well, since that's the term used the last time I was still working for/with people in chairs, and nobody has offered a different term for people that can't get around without a chair, I'm at a loss to why the terminology should change.
You can be bed bound still.
You do understand there's a difference between a chair being one of multiple options and one being the only available option, right? Like, a person can have mobility issues where a chair is the best option because of pain levels, safety, etc, but could still use other mobility aids. And then there's people that have no other options (as of yet, regarding technology development). The term chair bound has no meaning other than that, that I've ever seen.
Secondarily, considering the term is also used by chair bound people in my disability and chronic pain support group, idgaf what some random internet site says.
Also, I am bound to my damn legs. If they disappear, I either drag my ass everywhere by my arms, or I get a damn chair. I'm also cane bound at this point since the risks of not using it so far outweigh any possible reason for not using it that it reaches absurdity to call it an option.
Some things are just dumb when it comes to nitpicking terminology, and this is one of them