If it were Beijing, you'd have comprehensive action occur within a day or two and it would be a strict policy enforced by the government. All Chick-fil-A locations would be shut down immediately and whatever was upsetting would be removed (or the chain would never reopen); and while the authorities are at it, they might go ahead and engineer a forced ownership transfer for good measure.
I'll note that Chick-fil-A is booming in the US. It's now the third most successful chain in the US by sales behind McDonalds and Starbucks. That's despite their non-PC position on gay rights.
The image of English-speaking westerners talking about "liberate hong kong" is a bit triggering for the average Chinese person, due to Hong Kong and England's history. It must be incredibly easy for CCTV to point at that and say that it's just the western imperialists trying to take HK away.
China promised 50 years of "one country, two systems"-- people in Hong Kong want to cash that check.