@myBTSims There's nothing in your hwinfo log that would definitively explain your computer crashing. Your processor runs quite hot, over 90º C, but that's not surprising. And it was a few degrees cooler than its max when the log ended. Your computer was handling its memory swap fine as well, keeping about 800 MB of physical memory free at all times. So I don't necessarily think this is a memory issue.
How long exactly did the log run though? It cut off at 17:45, and if that's how long you played, that's all fine. But it would be interesting to know if the shutdown happened a minute or two after that, both because there might be some missing data (e.g. a possible temperature spike) and because the data not being logged is useful info in itself. But if you think that's about the right amount of time, then there's probably nothing else to see.
It's a good idea to run chkdsk though, in case you happen to find something. Hwinfo didn't report any disk errors either; I'm just saying it's worth trying.
You can attach the results to a post as you did with your dxdiag.