I can see where they are coming from though; I'm pretty sure the investigations of Internet usage that turn up on politicians desks contain pretty disconcerting information about the human condition.
It's really dangerous to go around calling democratically elected governments "autocratic". These people really do try, and there's really no indication that any government except maybe Hungary is bent on perpetuating their power. Calling them names just removes any incentives for anybody to do well: Why bother, if you're just going to be called an incompetent autocrat anyway?
Who have the first conversation that we finally see as "the Estonia government want x". The same I would like to know about the free trade agreements.
As a guess, it's due to the threat to Estonia from Russia, which includes Russian cyber attacks and propaganda. Russia has used propaganda operations very effectively in Europe and the U.S. If the U.S. has trouble protecting itself, imagine Estonia's situation.
In response to the same issue, earlier this year (IIRC) I read about a similar call for government oversight of Internet publication by someone high in the UK government (but I didn't hear about it again after that).
[1] http://www.npr.org/2017/08/21/544952989/rough-translation-wh...