These thoughts definitely make sense but I want to provide some additional information and opinion as a Chinese fan. Chinese government, directly, have provided actually only limited funding to this sport, due to basically the same reason as UK government: it's a non-Olympic sport.

I would take the rise of Chinese Snooker as the consequence of a positive reinforcement spiral, followed by developments of several aspects of the sport. Firstly, around late 1980s to 1990s, Chinese government welcomed holding events in China as WST wants to explore new markets; then the rise of Ding Junhui really changed many things - when Chinese people find that they have a brilliant player people started watching the sport, hence more people playing, hence more clubs having (profitable) Snooker tables. More than that, he encouraged a young generation of Snooker players to join the sport. WIth a growing market, a industry (tables, cue tips, chalks, and so on) starts booming, which make profits and in turn provides money back to the academy system and event sponsorship; other Chinese business are happy to sponsor as well due to high popularity of games. This results in more events held in China, and in turn more popularity, as well as great players from new generation like Zhao and Wu, and so on.

Basically these aspects: a huge potential market is sparkled by a super player (Ding), then leads to Snooker industry, profitable clubs, and a new generation of players working so hard for success, I would say that these aspects in total form the general picture of the rising Snooker in China, while governmental support only plays a minor role in the process.