the ESP8266HTTPUpdateServer class source code is so shallow. It simply puts together the httpserver and the Update system. I would treat it like an example and copy it in my project and modify as I need.
I didn't look closer on it until now. The ESP8266HTTPUpdateServer requires to upload the firmware to the esp8266, but there is ESP8266httpUpdate library, where the esp8266 checks some url if there is new firmware available for download.