They are giving credence to the idea that words can injure. I would have rather seen this phrased as "that some believe to be offensive or injurious". But I imagine this sentence was heavily negotiated.
I prefer the generally-accepted definition of "harm physically", as I assume you do, but clearly some people try to generalize the idea in order to emphasize other types of harm.
It's a debatable topic, there might be a little bit to learn from hashing it out, but it's mostly fluff. It's better to explore if this illuminates any actual disagreement on some concrete issue.
This sort of taking umbrage about word definitions is a factor in pretty much all major political spats, and I don't think it's going away by arguing about each term. You just have to define the terms in some way for the purposes of mutual understanding for an individual discussion. If the debate ends up just being bikeshedding the definition, walk away and find a better conversation.