This "disappearing cursor" or "flickering cursor" used to be a known problem with video drivers in certain games, and could often be fixed or made less noticeable by reducing video acceleration. That was with Windows 98, but it might be worth trying in Windows 8.1 if your video card's drivers allow it. Here's an article telling how to reduce video acceleration (aka hardware acceleration).
https://www.thewindowsclub.com/hardware-acceleration-windows-7I don't think the mouse would be the problem if it behaves outside of these games. If it's a wireless mouse you could check that its batteries aren't low.
Two programs that will generate lists of specs are the BelArc Advisor and speccy.
https://belarc.com/products_belarc_advisorhttps://www.ccleaner.com/speccyDo you know if your computer is set to automatically install video driver updates in Windows update? If it is, see if you can figure out if your video drivers updated around the time the problem started.