The title of the original FOX article is a little misleading, at least if the text of the article is to believed. This seems to be an effort to change the vocabulary the City of Seattle uses. Which is perfectly acceptable. City officials can choose to do so, and they can decide how politically correct they want the city to be and what words to use and not to use.
They don't seem to want to limit the words that the public at large can use. Only those who are employed by the city and, then, only in their official capacity.
If they wanted to limit what citizens could say, well it's quite clear that would be a non-starter, but even such a thing,
somehow passed, it would be null and void anyways because of the
Supremacy Clause.