I wonder if Phoenician Gold meant Regional Powers. I don't know if I'd agree with that--the Delian League was arguably a regional power, albeit a relatively small one. Carthage was as well. If it means influencer, then it's just false. The influence of the Phoenicians on the Greeks alone is enough. I don't know if we can say with certainty that any one state was paramount (though, it would almost certainly be Tyre)
What I mean is that generally the individual city states influenced each other more than they influenced neighboring powers, and usually their impact is viewed collectively rather than individually.
Yes, Athens and Sparta led Greek leagues, but the city states themselves didn't really hold land outside of Greece, establish colonies, make alliances, conquer. Their cultural legacy bled out but ultimately they never became superpowers outside of Greece. And even as we remember Greece, it was strongest not when the city states were. divided, but when they coalesced into Greece.
As for Byblos and Tyre, they were important to the Phoenician empire, but didn't do much on their own separate of the Phoenician empire. They were capitals, not city states going off doing their own thing, part and parcel of greater Phoenicia. The blobbing with Carthage kind of emphasizes that they were are all parts of a greater polity more than they were individual powers.
By contrast, just Venice or Genoa
alone established the same scope of colonization as Phoenicia, completely separate of the other Italian city states and indeed each other. Their accomplishments weren't limited within the larger Italian identity, they were minipowers existing and competing alongside other kingdoms. It is much easier to treat them like individual civs because they a) were more strongly individualistic and b) never really represented either a league or a collection of colonies or any sort of cohesive community.
At the very least, even if we were generous and said that Athens and Sparta (and Corinth and Thebes?) were as influential outside of Greece as the Italian city states (or Byblos, Tyre, and Carthage)...they didn't have as many as Italy did and by the fourth city state you're already struggling to find another city to found with the same degree of power and identity. Whereas Venice, Genoa, Florence, and the Papal States were each HUGE powers, and Bologna, Milan, Naples, and Sardinia were only slightly less so.
The difference is that Italy at its strongest stillswasn't Italy. It was Florence, Venice, Genoa, etc. That is how much more influential those city states were individually than Greece or Phoenicia.