Agree completely on the important part being respect and empathy. Agree on the second employee’s tone seeming argumentative. However, from the given information it’s not clear if the original (fired) employee remained respectful.
There’s no ambiguity if the firing was only about the original comment - that screenshot however is missing possible further comments from the fired employee. If the discussion turned disrespectful (e.g. personal attacks), that could explain why HR did the firing yet had no issue with other instances of the word “nazi”. Still probably not a justified firing, but would make more sense.