Wiktionary gives the meanings "at least one" and "no matter what kind". The first likely doesn't apply here, as it's not used in a negation or question. To interpret "no matter what kind" to mean "every" seems like a stretch to me. I really do think the meaning of "any" is ambiguous here. "any" just specifies that we don't have any further constraints on x. You could replace it with "every" or "at least one", but not with "every even" or "at least one even", as that would introduce a new constraint.