So I've been going back and forth about this for days now trying to get it to work. I run the game on a Win 10 Pro 64bit system. So it seems a combo of the different sulutions given here and there did seem to work with a few tweaks.
Here is what did it for me.
Fresh install first.
Head to the origin game page and find RA2. Go to game properties and disable the Origin UI in game and also add "-win" in the command window above so the game will start in windowed mode.
Then install and copy this ddraw file found here. Extract the rar file in the root RA2 folder. If you used an origin install, it's most likely in "C:\Program Files (x86)\Origin Games\Command and Conquer Red Alert II" Included in that rar file was a dll file, but also a config file called aqrit. Open it with notepad and only change "NoVideoMemory" form 0 to 1 only.
Then we need a launcher fix found here. Simply run it and select RA2 form the list and patch it.
Now you need to go RA2 install path again and find the game.exe and gamemd.exe. Go to properties on them and make sure they both have Windows XP service pack 2, reduced 16bit color mode, and run as administrator.
Lastly we need to edit the RA2.ini file. As now the game should work and run fine, but in a small window. If you go to the RA2.ini file and find the [video] section. You can edit the screen res there to match your desktop one. I had some small screen issues, but jogo_veio's trick and extra video options fixed it. Here is what he had added in his
[Video]
AllowHiResModes=yes
AllowVRAMSidebar=yes
VideoBackBuffer=no
ScreenWidth=1920
ScreenHeight=1080
StretchMovies=no
Simply copy that into your own RA2.ini file and adjust the screen res to match yours if it is lower.
That did it for me. Now the game runs in HD in window mode with working cinematics that has the correct colors etc in Win 10. The only issue is that the screen might flicker if you have something behind hit, like a browser window etc. Just make sure to hide all windows on the screen the game will run on first. Then I had no issues at all running it.
Oh and I know if you need to do a fresh install. You are forced to watch the intro again. 2 ways around that. Either crash the game and close it with task manager when the intro starts. It still will think you have seen it, and will skip it the next time. Or add a new line in the RA2.ini file right above [serialDefaults] all the way down. And simply add
[Intro]
Play=no