The initial problem with the laptop was when I started to play League of Legends on it. It would run for perhaps 5 minutes and then the laptop would just instantly turn itself off (and wouldn't start back up again until the power supply was removed). So I ran Prime95 to see if it was a CPU problem and it ran fine for ~1 hour with the CPU peaking at 96C. Then I ran Furmark at the default 720p benchmark settings and the problem occured again within 30 seconds. Obviously it's a problem with the integrated GPU so I decided to check the drivers.
On my device manager it lists it as 'Intel HD Graphics Family' and it's version as 10.18.10.3304 but on the Intel HD Graphics Control Panel it lists it as Intel HD 4400 Graphics, with the same driver version. (Not sure if this is relevant but it might be)
So I went to the Intel website and downloaded the correct driver and tried to install it using the .exe. I then get this message. So then I tried to manually install the driver from the .zip, and get this message.
Essentially I'm wondering why the driver won't install and whether or not it may be the cause of the instant shutdown problem that only occurs under intense GPU stress.