Punisher 2099 was fascist (Wouldn't kill cops, and became part of Doom 2099's regime when he took over America.) but Frank Castle Punisher (A.k.a. the one we know.)? Pretty much equal opportunity murderer of criminals and baddies.

I assume they mean "murderer of fascists?"

A fascist is someone who supports a single strong leader with total control of the nation. 'Dictator' was an actual position in the Roman Republic; the people could vote to give one man absolute power for a period of time. Makes sense if you're dealing with a natural disaster or invasion and don't have time to go through the usual channels. Fascism became popular in the chaos of the post WW1 era. Things were changing rapidly, and conservatives wanted to rein in the 'undesirables.' Ironically, the Communist Russian Revolution was a huge spur to the creation of numerous fascist parties across Europe.

Frank Castle, the Punisher, is not a fascist. He isn't interested in taking power for himself, and doesn't want a dictator. He often speaks of having the greatest respect for Captain America, the guy who always chooses the side of liberty and fair play. Frank knows that he's a criminal and a murderer. He just doesn't care. IMHO if he and the Joker were both locked up and unable to kill each other, the two would get along fine.

I don't really see how he could be construed as one, other than the kneejerk "fascism is when bad things".

The whole point is that he's not like cops.

How fascist he is depends on who is writing him. His symbol is literally a stylized Nazi totenkopf, and while he has never voiced support for totalitarian leaders, his solution to crime - escalating the violence - is consistent with fascist ideology.