I said “Mental state” on purpose in the definition, because the question you are asking isn’t relevant to the point at hand.
Describe behaviour by behaviour, don’t give it a label unless the person in question has labelled themselves or been reported as that label elsewhere. That applies to everything in the listed FAQ, not just mental illness.
“That person seems to lack empathy and really seems to be a narcissist” is just as informative as trying to shoehorn a label onto their behaviour - perhaps more so, because the reader doesn’t need to have previously been exposed to the label before.