I wonder whether everybody, who is willing to vote in the contest is required to create an itch.io account or use a GitHub-account?  Is there any possibility to vote without those accounts?

I have no control over it, but I guess itch doesn't want voting to be flooded.

So not only you need a registered account but, if the account is too new, they will make you vote random entries before you can select one.

There's even the option to limit voting to those who participated in the event, but I found it too harsh, especially considering the various languages.

Exactly, to be honest I find this voting system too harsh, doesn't keep into account several things, but oh well, was fun anyway.