What I understand from the caption that he says the window cracked at FL
450,he doesnt mention flying the rest of the flight at FL450.
I can not comment without seeing the QRH of the Gulfstream III on this incident,still I am sure they handled it according to the requirements and limitations of their aircraft
My A-321 QRH limits the max FL
at 230 in a cracked window situation.
Don't mix the total cabin pressure loss with this situation since you still can control the pressurization on a crack windshield problem.An emergency descent to 10000 feet or highest alt on the route is required only when you cant control the cabin pressurisation anymore.