Hello, I get the same issue during one of the cutscenes mentioned above:

"Extinguishing the Last Light" Cutscene #7 - Right as the Crystal Exarch's hood is blown back.

and I can reproduce it when viewing the cutscene in the Inn. The way I got past it originally was by clicking off my screen thus causing the FPS to dip to 15 (my inactive client FPS setting is set to 15). My GPU temps/usage did not get very high (I have an RTX 2080TI) so I'm not sure why clicking off even helped, unless it was just luck.

I have, however, also gotten this issue in another game so I'm unsure if it's FFXIV specific. I ordered a new power supply and will try again when it is installed.

The event log says: Kernel-Power ID 41 for the Critical issue. "The system has rebooted without cleanly shutting down first. This error could be caused if the system stopped responding, crashed, or lost power unexpectedly." which isn't terribly helpful.