I believe there are two separate axes. You can have a free market without civil liberties (i. e. Singapore, or Germany ca. 1933-1945), or a less-free market with civil liberties (maybe the Nordic model). "Dictator" is really only concerned with the latter, apparently, although I have always associated it with the political right.
You're right in thinking that it appears hard to be truly democratic without (some form of) a free market. At least I can't think of an example. And I've met many eastern Europeans with an aversion to even slightly left-of-center economic policies because of their history. But communism doesn't have a monopoly on being terrible to its citizens.
A system of authority and security does not operate at an economic level of autonomy. A regimented heirarchy differs from the conceptual model of interaction among autonomous individuals and organizational collectives.
Replacing "communism" with "government" may be just as accurate.
I live in UK now and it's absolutely terrifying how every move by the UK government reminds me of the stories told about the communism back home.
Sure, communism itself might not be about reducing democracy, but I guess it would be very hard to find an example where it didn't.
Edit: ok, according to wikipedia, I'm wrong:
https://en.wikipedia.org/wiki/Polish_United_Workers%27_Party
"Until 1989, the PUWP held dictatorial powers"