I agree that if you're moving the goalpost to just take-home salary being in the global 1% is less meaningful. Someone with no assets and a $20k salary in NYC is dirt-poor, but if you've got that salary in say Morocco you're relatively rich.
But in your earlier comment you mentioned property ownership in some of the most expensive markets in the world, which is entirely different. That implies that you own hundreds of $K of an easily-sold asset, and you're only "poor" to the extent that you're unwilling to move.
As I noted the same could be said about someone with a penthouse in NYC. If they own a big part of a $10 million dollar house and struggle to make mortgage payments they're poor by this narrow definition, but of course that's an absurd way of looking at things. They can simply cash out and move somewhere else, unlike someone who's actually poor.
Being rich and having expensive tastes doesn't make you poor, it just makes you selective.
Still, to address this specific example of yours. Even someone who's struggling to get by in an area that's in the 1% of income worldwide is in a much better situation than someone who's struggling proportionally as much (when adjusted for purchasing power) in a much poorer country.
They're going to benefit from better public services, their kids will go to better schools and have better opportunities etc.
I think once you account for all of that the picture isn't going to look significantly different than if you'd just have looked at salary with no regard for local purchasing power.