This happend three times to me so I know this is a problem. After around a minute or so playing on the map, my PC hard shuts down. As if power to it was suddenly cut. I think that my PC was protecting itself from a fatal crash, one that could damage hardware

This seems like a problem that may be beyond your control. I mean, I dont have acess to the project files, but it seems to me like there is simply badly written code in the game engine itself (unity right?). That being said. I think you should have a talk to the unity community itself about this. I'm the only one who seems to be having this problem, so I do not think this is a software issue, more and more, this seems like a hardware issue.

My motherboard is a Gigabyte 970A-DS3P and my graphics card is a GTX 980 TI, CPU is an AMD FX-6300, and yes, I am running the linux version