The API in bmminer and cgminer and a few other ones, was designed by me long ago.
It's a simple API that imposes very little overhead on the miner due to the design, since the miner's job is to ensure it does as much work as possible and gets the work results to the pool as quickly as possible.
It's nothing to do with the pool.
It's in every miner from Bitmain and Canaan.
Argh... And I wrote a complex php script using curl to "log in" to my S9 / D3 miners to monitor and reboot them. An api would have been much easier! Are there reference docs that are easy to find on the web? Bitmain's site does not have a lot of help documents that I could find.