In the novel, I believe the government is just a front. All we see it doing is perhaps making decisions on the leading of the country. I see more of a governmental role in the firemen than the central government itself. The firemen are enforcing the government's rules. It doesn't seem like the people are as afraid of the government itself, but more the firemen who are actually burning the books.
If they really had a vote, I doubt the people would vote for anyone who supported the burning of books...BUT maybe the society was so used to it that there were no other options. The main role of a government is to serve the people and I don't see that in the novel. I feel like the government is doing an inside job and just trying to avoid free speech and expression. So if you had to classify their government, I would say it is a limited democracy but it's not that similar to the U.S. democratic republic.