Well the shrt cct in the igbt will not be for long otherwise it would blow, so the short circuit , when it happens, acts like a kind of step input to the intrinsic junction capacitances of the igbt, and as the diagram shows, there are trace inductances in there which can form a resonant circuit with the igbt capacitances, so its nice to put the cap in there so as to prevent really high frequency oscillation which switches the igbt gate on and off really quickly and cause too much switching loss….so you are slowing that process down basically, and reducing subsequent switching loss, and the RC filter is damping it out too.
- - - Updated - - -
Its one of the niceities of igbts that they can switch off a short cct current and still survive, but as your doc tells, you still need the RC filter to damp out the violence of the sudden short circuit, and indeed the violence of the sudden switch of of the short cct by the igbt……as you know, shrt cct is pretty drastic..not surprising the onset of it can involve massive amounts of bad-boy ringing