G V gear operated off left hydraulics. If no pressure in left side PTU will auto on to repressurise left using right side pressure. (PTU can be switched off if req.)So shutting the right would have no effect and I have no idea what good shutting the left engine down would do. If no left system hydraulics you can blow gear down with emergency system but this would leave the gear doors open. I didn't see the footage..... did anyone notice if the doors were open?
Flight Safety...After take off I would guess that the CAS would have annunciated that the right door was open plus the red light in the gear handle gear would have been on. I imagine the pilots relayed that info when talking to maintenance.