I think we are confusing the functionality here... an API call is a GET, almost by definition. There is nothing that AMCrest could add to their API that would effectively create a "PUSH" notification. What is missing in this equation. and what I was referring to in my previous comments, was the existence of a web service (or cloud service) that would receive notifications from the camera and forward them to ST.
I do not believe this will ever happen with most IP camera manufacturers as it would require their writing some form of interface from their cloud service to ST, or the introduction of some form of "hub" for AMCrest IP cameras (similar to the Blink paradigm).
All of that being said, using something like Blue Iris and coding some kind of Perl script on your own web server to effectively push notifications is certainly possible, but it is waaay outside of my available "free time" to code.
And, as I have pointed out several times before, you can get around many of these limitations by using Open/Close sensors wire to the external Alarm hard-contacts available on some AMCrest camera models, you can use IFTTT to act on emails received from individual cameras, etc...