You may use it without receiving specific permission from Mozilla. Only trademarks are protected.

See Mozilla Trademark Guidelines.

I am not sure if this solves my problem. If I want to use that screenshot on Wikimedia Commons or Zenodo repostiories, I think I still have to provide a license. They would not probably accept simple statement "no specific permissions". But if you say its "public domain", that would sounds me and I would know what to do with that. Or is it Mozilla Public License 2.0 too?

Yes I guess it's MPL.