It’s an English invention, like many other widespread games. Why is it so big in China? Wikipedia says it’s the most popular amateur sport in China. Why didn’t other games like soccer and cricket take off as much?
Possibly because it doesn’t require much space? They might not want to devote valuable land useful for other purposes to cricket pitches or soccer fields.
It’s pretty fun too.
IIRC there was a government backed push to get people to play ping-pong in order to show that Chinese people could excel at sports. Presumably it was chosen because it is a sport that people with the average Chinese build would excel at.
The space thing is surely also a factor. Any given urban stadium on any given evening may well have a few hundred people out walking in it. It can be very difficult to find space for casual footbal games.
Besides ping-pong, badminton and basketball are also quite popular. Both these sports can also be played in relatively small spaces.
People that are small in stature with lightning quick reflexes. What could be better than table tennis (not ping pong)?
If only they could combine women’s nude gymnastics with table tennis (sort of like beach volleyball) then we would have a real sport.
Chinese people like ping-pong because, the name of the sport is really easy for them to pronounce. 
What’s not to like?
Why not ping pong?
It was chosen for precisely that reason.
The old Soviet Union Government did exactly the same with chess, because they wanted international prestige.
The Chinese also took the recent Olympic Games very seriously, spending huge amounts on training athletes, building stadiums, having lavish ceremonies etc.
If you show a politician an opportunity to get publicity for themself, the funding will instantly appear.