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).