The democracy index is a composite score built from sixty variables organized into five dimensions. I downloaded the reports from 2015 and 2016 to compare Turkey's scores.
My summary is below:
Overall, Turkey's score dropped because of changes to their electoral process (which includes pluralism) and decreases in civil liberties.
The civil liberties score was already abysmal. The scores used in the democracy index are broad indicators, not exact measurements. These two factors combined mean that even if Turkey substantially curtailed civil liberties, that part of their score likely wouldn't change very much (because it doesn't have very far to drop, and because the measurements don't work that way). For example, the first variable is a single question "Is there a free electronic media?" Country's get 1 point if the answer is yes and 0.5 points if there does exist a free electronic media, but it is dominated by the state or a few private owners.
The electoral process score also decreased strongly. Many of the variables here have to do with the fairness of elections and pluralism. A strong decrease here matches the expectations in the question.
The functioning of government score increased a lot in this year. This largely offsets losses in the electoral process score. Why did this increase? We don't have access to the specific scorecard for individual countries. However, many of these questions are not particularly reflective of "democracy" as you might be thinking of it. For example, several of the variables here are thermometer ratings from the World Value Survey ("Do 70% or more of people have a great deal of confidence in the government?"). Additionally, questions like "Does the government's authority extend over the full territory of the country?" and "Do [special interests] exercise significant political power?" increase this score, which is perhaps not obvious from its label.