I'll also note that nothing here is per se undemocratic. Both the Parliament and the Council are made up of elected members. The members of the Council (as members of the national governments) are indirectly elected, but elected all the same. Direct election is not a requirement for a democracy (see election of the US president or the US Senate prior to the 17th amendment or the Senate of Canada right now).
That does not mean that there isn't plenty of valid criticism of the EU's current structure, but claiming that it is not "actually democratic" falls far short of a meaningful critique.
Note they wrote "Start by removing...", not "Finish with". You could remove Council of the EU and then create another "upper house". But its personnel would have to be nominated differently. Perhaps directly elected? But that would be tough.
Re the direct vs indirect election, note that in some countries governments do not have to consist of MPs. Like currently in France, you have a directly elected president who then nominates whoever to be his head of government and ignore the parliament for a while. And that government has a say in the Council. And at that point it's good to answer the question, at which level of indirection can we say there is a deficit of democracy?
Also note that it's quite unusual for a democracy that the 'lower house' (EP) does not have legislative initiative, can't propose laws. Is that a deficit of democracy yet?
Of course I understand it's all because national governments do not want create another centre of power, but the issues are very real.