In theory you should be able to do it by loading a hacked color profile into the video card's LUT. Almost all video cards have a LUT (lookup table) for supporting color profiles. The original purpose of a color profile is to correct small color deviations in your display hardware, so artists and photographers can edit their work knowing that the colors are accurate. However, you could program the LUT to simply take colors difficult for color-blind people to distinguish, and reassign them to colors easy for them to distinguish. It is after all just a big table mapping one set of colors the computer sends the video card, into a different set of colors the video card tells the monitor to display.
A quick Google search based on this idea came up with this page. It's a couple years old so I've no idea if it works, nor how to make it work. And I'm not color-blind so even if I tried it I wouldn't be able to tell you if it works. You'll have to try it for yourself.
https://github.com/nelas/color-blind-luts
The fly in the ointment (you knew there would be one right?) is that most games don't play nice with color profiles. Color profiles work fine with Windows desktop programs, but games which flip the display into full-screen mode usually dump the color profile in the process. You can avoid this if you play the game in windowed mode, but that can lead to poor mouse control in some games.
It seems like there was a kickstarter for a similar idea - a box which sits in the video cable between the source and the display, and remaps colors to ones more suitable for color-blind people. But it never got anywhere.
https://www.kickstarter.com/projects/1217951813/digital-video-lut-box-for-colorblindness-correctio?ref=category_newest
Based on my quick research, I'm a little frustrated by the state of things too. Based on what I know of color profiles and LUTs, this would be rather simple to implement and would help a lot of people. But the only ICC color profiles I can find are for simulating color blindness so regular people can see what your vision is like. Not for remapping existing content to a color palette more visible to color-blind people.