You seem to be conflating the statement "drawing talent from across the world" with something more akin to "drawing talent from the entire world". Of course hockey doesn't deeply penetrate the culture of nation on earth the way a sport like soccer does, but the fact remains that there are currently players in the NHL from 18 countries. It may be a niche sport in a lot of these countries (eg. in Australia where Nathan Walker is from), but there is at least some footprint that leads to some people from that country being exposed to the sport (Australia even has a hockey league of its own) and having the opportunity to learn to play the sport (and modern travel also makes it possible for these people to have access to high-end training in junior systems like the CHL and its feeder leagues). In 1920 for comparison, the NHL had players from merely 3 nationalities: Canada the UK and the US and of that, over 90% were Canadian. Hockey will always remain a niche sport in any country where there isn't freezing weather in winter, just due to the fact that the environment makes it way more likely that people there looking to try a new sport will go out in the warm weather and play another sport instead of seeking out the nearest ice rink (which may not be close), but despite this, it would be a mistake to underestimate how much further Ice hockey's global reach has expanded in the past century. Now if you want to compare hockey's footprint in 2020 with hockey's footprint in 1980 or 1990 then that is a different discussion. However I specifically say 1920 in the post you are responding to.
Semantics aside, one fringy NHL player from Australia who played juniors in Europe doesn't make ice hockey a global sport. Fact still remains that:
Asia, population: 4,5 billion | NHL players from Asia: 0
Africa, population: 1,2 billion | NHL players from Africa: 0
South America, population: 422 million | NHL players from South America: 0
So there you have 75% of the world population (6,1 out of 8 billion) on three major continents producing the whopping number of zero NHL players.
Yeah, I know they play hockey in Korea and Japan, and that's great, but I'm not entirely sure how it makes the NHL in 2020–21 a better league than NHL in 1995–96? I'm dying of curiosity here.
When the Iron Curtain fell and all the Soviet and Czech players could play in the NHL (Hasek, Jagr, Mogilny, Fedorov, Bure, et cetera) in the 90s, of course that made the league better (the league, not necessarily the sport, at least not to the same degree) to a certain degree. But that's because the Soviets and the Czechs already were very, very good. They didn't magically turn great overnight just because they were given the opportunity to play in the NHL. They already were serious and proven top notch hockey nations. There you have something tangible you can point at, regarding top competition and influx. Korea, Japan and Israel in hockey isn't top competition and they aren't producing any NHL players in 2020–21.