If you have a definition of fascism that wouldn't include this, I would be very interested in hearing it.
While having secret police arresting people for no specific reason -- "gang of thugs doing whatever" -- is a feature of every fascist state I can think of, I don't think it's a necessary component. I always thought it was a way for people to swallow the horribleness of the state as the messy bits will be more concealed. It might be even scarier if they didn't need one, honestly. Imagine you're in a bowling league and uniformed thugs arrest Mel in the middle of a perfect game, exclaiming "Mel called the fearless leader a stink ass on MySpace last night, he's going in the clink!" to which all his friends nod in agreement and say "well fuck you Mel, what are you, a capitalist?"