What do you mean by "so many"? Singapore appears to be an amazing success story in containing C19.
They are using aggressive contact tracing as part of that, so if it were spreading like wildfire through A/C vents surely that wouldn't be effective and they would have a much faster growth rate of cases.
I don't think the assertion is that it's spreading through vents, just that spending time in a very air conditioned room mimics some of attributes of winter that make the spread of respiratory viruses more likely (dry air, dry nasal passages)
There may be something to this. If you look at the actual cases in Singapore, they seem to be clustered around two specific locations, one company and a single event which I would presume was held inside a single big hall.
I'm in Singapore, and life here goes on pretty much as it always has. Except for a larger than normal number of people wearing masks, you can't really tell that this is ongoing.
That said, the government is doing a lot to keep it that way. There is intensive contact tracing, and companies register people going in and out of their offices (to help tracing), if you're sick you're supposed to stay at home, and so on.
They are using aggressive contact tracing as part of that, so if it were spreading like wildfire through A/C vents surely that wouldn't be effective and they would have a much faster growth rate of cases.