Having seen a few documentaries about China and Chinese society I can imagine it went something like this:
After failing to extort funds from the company the scammer finds out where BTCGarden are based and discovers he is in the same city.
The scammer starts bitcointalk campaign and convinces other forum members to complain via email/phone to the local Police station.
The scammer visits the local police and charms them into action based on his and others complaints. He could walk into the station and claim he is a local businessman, throw them a small bribe, and they will take him on face value, put 6 Police in a van and go tell BTCGarden to close down. No investigation, no more questions asked, simple as that. If BTCGarden had put up a forcefull defence they could have persuaded the Police they were legit but with multiple complaints it's easier for the Police to accept that 'evidence' and threaten action if their demands to close aren't met.
We would call it corruption but the attitude of the Police is tied up with the old secret state and the heavily oppressive days of non-reformist Communism. There is still a lot of fear of authority in China and if this scammer is a recognized member of a local Communist committee he would be able to easily influence the Police. Or he may have a cousin working for the Police and you'd get the same result. Remember China is still a Communist State, a progressive one, but it still has a lot of institutional corruption. For these reasons I can believe the BTCGarden story. It may be false but it is entirely possible.
This scammer guy now has some proven history and he will use this success in his next venture into btc extortion. That doesn't mean he would be successful trying to shut down other China based btc companies, it would depend on if he could influence the local Police where the company is based. China is a very very big country and I doubt Police would act on email accusations, he would have to visit the Police station to get them onboard which would not be worth it if that is a great distance from him. Also other companies may have more well connected founders - so if there is a Communist committee member in the family who could back up the company directors that would ensure there would need to be a full investigation - there would be no 'shut down now' order - and the investigation would find no wrong doing.