Sachin's popularity is mostly limited to India and, beyond that, almost entirely limited to the British Commonwealth. Of course, the Commonwealth is quite large, but outside it, Sachin is not only not an icon, he's completely unknown.You definitely nailed the most extraordinary part of his popularity. Roger Federer has a similar effect on people in tennis, but it is definitely very rare to see.
I think you're severely underrating the extent to which a nation of over a billion people worship Sachin Tendulkar as something not much less than a god, for performance in a sport that is more popular there than american football is here*. But other than him, and maybe other top-5 global soccer stars (Ronaldo certainly, Neymar has his following, Zlatan until recently, maybe Kane, Pogba, Griezmann...), it's probably not a long list among figures today and in recent memory.
Extend it back to the dawn of global sport and sport fandom, though, and I think you'd add a lot more names to the list. That's probably the start of the 20th century (football in europe, baseball and gridiron football here, plus cricket throughout the commonwealth, and the olympics once you get into the 1920s). Maybe those names wouldn't come from golf, basketball or hockey, but certainly in boxing, and perhaps elsewhere too.
* 64% of viewing sessions of sports in India are of cricket.
Of the current soccer stars, only Messi and Ronaldo have really reached the Ali/Jordan level of transcendent global fame. Maybe Neymar is not that far behind them. Certainly not Kane and Griezmann. 15 years ago it would have been Zidane and Beckham.
It's hard to compare pre-WW2 to post, the world was a lot less integrated culturally then. If we're going back pre-WW2, globally, then maybe Donald Bradman (at least within the British Empire), Joe Louis, and Jesse Owens would get considered. There were no real global soccer stars pre-war, certainly nothing like Pele.