Red Alert 3 uses SecuROM as DRM system. All support for SecuROM was specifically disabled on Windows 10, with Microsoft citing it as a security risk. On Win7 and Win8, this was done through a system update, meaning it could be circumvented by specifically uninstalling and blocking that update, but in Windows 10, the system was simply never included in the first place, and the only known workarounds for Win10 are some hacky manual way of reinstalling the missing SecuROM drivers on the system.
An easy solution is to redeem the game key on Origin; that'll permanently link the game to your account and allow you to use the downloadable version. I'm honestly not sure whether keys are specifically identified as Premier Edition though, and whether the online version would thus give you any specific bonuses the Premier Edition would give you.
