How to get Company of Heroes to work on Steam with Windows 10:
I found the solution to the problem:
1. Go to the folder where you have COH installed and look for RelicCOH.exe
2. Right click on RelicCOH.exe and select Properties. Select the Compatibility tab and check the box that says "Disable fullscreen optimizations"
Link to the solution on Steam: https://steamcommunity.com/app/228200/discussions/0/3182216552765743658?ctp=3