Try Aida64 Extreme. Go to tools > System Stability Test
Check all tests less local disks and click on *Start* at the bottom left corner.
Go to voltage tab in the centre of that window and check what's the lowest voltages you get, if it drops too much that might be the problem...
My PC also started to shutdown on just a few games and others don't, on my case it's the 2 Motherboard connectors or the PSU cables that aren't connecting much good, I had a big drop in voltage when both the CPU and GPU is stressed, I had to open my case and keep moving the 2 motherboard connectors with my fingers until I get good voltage and no more shutdowns on my case and after some time of my room door keep hitting the chair where my PC case is, it goes to shutting down again, so I have to open it up again from time to time and check the voltages again and keep messing with the cables until I get again good voltage result.
But it can also be other things on your case, bad CPU or bad motherboards also sometimes cause that. You could also check motherboard VRM temps and the whole motherboard temp sensors with the software from it's brand and see if something's wrong with it... On my old PC I have a big OC and I have to add a motherboard assist fan to keep the VRM and all motherboard parts cooler (this is rare for a old motherboard non PCI-E 4.0 to need a motherboard fan though, but on mine it says to put a fan when OC).
