Loitering around
I think the idea is that launch detection is performed by aircraft like this anyway, so strapping a laser on one that can kill (and energy levels needed for a kill on a pressurised cylinder of liquid oxygen and other volatiles are fairly low) at the same range as the detection kit works is not a bad bet.
I suspect the viability of the project is somewhere between the optimism of the designers and the pessimism of the sceptical though largely uninformed commenters here.