doubts about a coupled inductor
This is a variation on the "fly-buck" topology:

An isolated buck converter, also known as flybuck converter, is created by replacing the output filter inductor (L1) in a synchronous buck converter with a coupled inductor (X1) or flyback-type transformer, and rectifying the secondary winding voltage using a diode (D1) and a capacitor (COUT2). The topology can be extended to any number of isolated secondary outputs. It also can be used to generate one or more inverting outputs.

You can read all the details here: Flybuck Topology

The caveat for your schematic is that the flybuck will not work without continuous inductor current.

Your topology is using a buck converter as an inverting buck-boost for the primary load (your -15V), so that load current will have to be high enough to keep the inductor current continuous or the +15V rail will lose regulation. [Edit: This may not be true according to the app note linked by G36 (Good find!), since in buck-boost mode the duty cycle will be different from a straight buck.  You would have to run the calculations to be sure.]

The MOSFET is exactly as you described, a switch to turn the converter on and off based on the KILL signal.