I've read Popular Dictatorships. I'm not naive that they care about public opinion and have "elections." Having unfree and unfair elections is not the same things as having elections in a real sense. Party based FPTP elections are generally free and fair. There are real concerns about gerrymandering, but for the most part, even a gerrymandered area is effective as a political pressure release valve.
At play here is the difference between necessary and sufficient conditions for democracy to be genuine.
There are a vast number of ways in which people can be denied a legitimate opportunity to obtain the policies most want (making a democracy less legitimate), but to list a few:
* People are allowed to vote, but votes aren't counted fairly.
* The voting system can be vulnerable to vote splitting (e.g. First Past the Post) or have other vulnerabilities that can lead to an outcome where the majority would have supported candidate A over candidate B, but B wins. This can lead to dynamics where tactical voting means only the candidates endorsed by the two best known parties have a chance, even if both of those parties are captured by minority interests. Generally the duopoly perpetuate the poor voting system to protect their interests.
* The leaders of any movements challenging the incumbents can be targeted before they have a chance to run - e.g. with trumped up legal charges, defamatory claims, violence either blatantly from the government, or by supporters which goes unpunished / is pardoned.
* Voters fear that if they vote against the incumbent, they'll face consequences.
* Voter demographics considered less likely to support the incumbent face barriers to vote, such as demands to provide documentation they might not have.
* Special case: Voting is restricted to citizens, but there are populations of people who live long term in the country but don't get a vote. Citizenship is not granted to or even stripped from people who are considered less likely to support the incumbent.
* Media is state owned, and is biased towards the incumbent, preventing the public from learning about alternative policy platforms in a meaningful way.
* Media is privately owned, and biased towards the interests of the owners of the media, preventing the public from learning about policy platforms opposed to the owner in a meaningful way.
* There are significant barriers to becoming a candidate (financial, or requiring a lot of work which costs a lot of money), preventing non-wealthy groups from being able to run.
* Corporations or ultra-wealthy are allowed to selectively fund large amounts of money (beyond the means of normal citizens), allowing policy platforms they support to drown out policy platforms in the interest of the public.
* As you mentioned, electorate boundaries are set in an unfair way (gerrymandering).
There are a lot more - but the summary is that there are many ways to undermine a democracy, and there are many countries that are nominally democratic, but aren't really.
I'm Russian, so I'm speaking from personal experience here. The media did some work back in the day to get him elected in the fir place, but they made him into a "strong hand" because that's what the electorate demanded. The people weren't duped into voting for an autocrat; they were openly told that this is exactly why they should vote for him - and most did.
From there elections kept getting less and less free, but it was a gradual affair - strangle the opposition TV first, then newspapers, then finally start playing directly with electoral fraud; fake counting etc. The purpose, though, wasn't to ensure a win - his popularity was always sufficient for that. No, it was to make it a win so resounding that agitprop could refer to it as a definitive popular mandate. And for parliamentary elections, to get the supermajority they needed for constitutional amendments. But that is how authoritarian democracy works - the majority votes in the government that cracks down on political dissent because the majority wants that. No amount of free press or free and fair elections would change that.
Quick note that totalitarian states often have elections in which the population is allowed to vote.