Thanks!They never replied directly to my email, their response seems to have consisted of updating the product page on their website and including, among other things, a reference to their wireless 'USB' chime which vandyman mentioned:
Wireless chime receiver for smart doorbell camera
The 'USB' part of the chime is just that it gets its power from a USB power supply.
There does not seem to be a way to connect it to an existing chime, you'll have to use theirs. As I mentioned in a previous post it might be possible to open up their chime and with some additional electronics connect an existing chime or, perhaps with an Arduino or similar, have it send an event to BI. Both options, if possible, will require some research and will be be fairly involved. For now I would say your only option is to use their chime as is.
I was hoping for a pair of ('undocumented') isolated connection points which are being shunted by the button.
Anyway, I am contemplating ordering the doorbell and once received examine the internals (PCB) for any clues.