EU commissioners are indirectly elected as they get their nomination and mandate by the elected governments of the members. While they hold considerable powers they're also kept in check closely by the European Council and the European Parliament, which are both democratically elected entities.
We don't directly elect our ministers, we don't directly elect our chancellor, you don't directly elect your ministers and you don't directly elect your PM, but suddenly it's a problem when EU commissioners aren't directly elected?
I appreciate that we're talking about the subtlest of differences here but ministers are pretty much always democratically elected officials (in that they hold an elected role). There are some exceptions, but they are rare. EU Commissioners are job applicants. There is absolutely no democracy involved in their selection, barring some of the interview panel being elected. Special advisors are then selected by the Commissioners. The equivalent of our civil service (the General Directorate?) are also obviously not elected, but hold tremendous power.
And I don't have a specific problem with it (although I do think it should be changed; EU Commissioner should be selected from MEPs imo). Just pointing out that The Kerbinator drawing equivalence between the selection of a PM and an EU official is misguided.