From that i can only read that you need some passport, not necessarily an EU one, that allows unrestricted worldwide travel and you need (thats a separate issue) the right to live and work within in the EU, which is a given for all EU citizens with a few exceptions for the newly joined EU countries.
Therefore an EU passport of course makes it easy to show that you fullfill both requirements, but there may well be other passports that can do the same.