Its an "open source" 64bit driver used to access "old fashioned" ports like the parallel port, serial port and others directly.
It is certainly not essential for running your computer and if you don't know how you got it, then its probably installed by some software you have installed, most commonly, Ive seen it used with software for controlling LCD screens. Do you have anything connected to a parallel port or serial port that requires special software to operate? There are plenty of other specialist things it *could* be used for but I would say its very unlikely to be "common" everyday use type of software. I have heard of people using it to send keystrokes and mouse inputs directly to the keyboard buffer at a low level so if you have anything that simulates keyboard or mouse movements/buttons, that would be something to check!
You need to find out what software is using it to work out if you can delete it without impacting your useage. If you search for Inpout32.dll or inpoutx64.dll on your hard disks, you may find that DLL along with the software that is using Inpout32.sys. The InpOut32.dll is responsible for installing the .sys driver file, and I would expect it either to be with the software thats using it, or in the Windows\system folder (which will make it less easy to work out whats using it!)
In theory, (usually) deleting drivers is not quite as simple as deleting the file. however, with InpOut32/x64 the driver is only loaded when the software using it is running, so you are probably safe to just delete the file. If you can't delete it, then you will need to uninstall the driver first and thats not quite so easy! It does not show up in device manager because it is a legacy driver and windows 10 seems like it simply does not list it. So for now I will hope you can delete the file.
Regarding the BSOD itself - very odd - I would expect that the software using the driver must be running at the time the BSOD occurs (which may help you narrow down what is using it I guess). While its a very simple driver that does not do very much, it hasn't been updated for about 7 years so it may just not be 100% compatible with windows 10.
Please note, the driver was developed for 32bit windows by Logix4u (no longer around it seems) they open sourced it and I simply ported it (recompiled it) for 64bit windows (it sounds like you will have my port). Personally I haven't used the thing myself for about 7 years, but others are free to use and distribute it with their software - which is probably how you got it!.