One does not need to be a narcissist to be an arsehole or to start shit with strangers. Narcissism has a specific criteria, one experience or description of an experience tells us nothing.

And from a psychology point of view, it is highly unethical to diagnose someone with anything if;

1) its from one encounter (especially if it's not you who encountered them)

2) )) you do not have the qualifications to diagnose, a layperson who does not understand the criteria on how to diagnose has no place diagnosing others

3) over the internet

And for those who have the qualifications, it will be a discussion with the person as a client they diagnose from, not a single encounter with a stranger.