Cities have city centres, towns have town centres. I suspect less than 5% of world use your terminology.

A visit to my home town, City of Newcastle, is referred to as “ gannin doon Toon “. ( going down Town ) but the city centre is never referred to as ‘downtown’

So name a few of these world cities .

We in the UK don't. Not 'every city in the world' is in America

Only in english language countries.

"every city in the world" what he means is every city in the United States.

In Sydney we have CBD. No downtown here.

This sounds like you're using 'the world' to mean 'America'?

For people making various points; “downtown” is North American terminology. So this is only the case with specifically English speaking North American cities

This doesn't get said in the UK, it's a North American thing.