2013 Peugeot 3008 stablelising warning light comes on and cuts engine

Is this the dynamic stability control (DSC) and traction control system / Anti-slip regulation (ASR) light or another ?

Yes it is

Many possible causes unfortunately , needs scanned to get fault codes and see what is triggering the light

The Peugeot 3008 dynamic stability control (DSC) and traction control system / Anti-slip regulation (ASR) help to keep the vehicle stable when accelerating and when cornering. Though DSC is always on by default at each engine start, it is only in operation when the warning light flashes.
Flashing: DSC is in operation and attempting to stabilize the vehicle.
Fixed on: DSC has a fault. DSC uses the same sensors as ABS meaning the DSC and ABS light may come on simultaneously. You can continue to drive the vehicle but without these safety features. Drive with caution and have vehicle fixed as soon as possible.