Running as administrator may not fix it. Starting the secdrv service (then shutting it off after you are done with the game due to security concerns) seems to work for some people, but not all. More info on that page.
Not that it matters because I’m reasonably sure the question has been answered but why the Game Room? If instead of Civilization 4, it had been Windows Media Player, would you have moved it to Cafe Society?
The basic problem is that Civ IV used a DRM scheme that is no longer supported by Win 10 (I think)
Firaxis (up until June 2017, unfortunately) were offering to send a free Civ IV Steam key to anyone who still had the original discs. I sent them a photo of the packaging, carefully posed with a piece of paper with my email address on, and they got back to me in a few hours. Alas, this option is no longer available to you.
Yeah, Civ IV (and many other games) used a DRM system called SafeDisk to enforce having the original CD in the computer. In 2007, SafeDisk was found to contain a security vulnerability that allowed malicious software to compromise your computer. In 2015, Microsoft released an update that disabled it on Windows 7 and 8, and blocked it from running in Windows 10.
Other people have already addressed the game-specific issue, but this raises a more general computer-security red flag – you really ought to have separate user and admin accounts and log into the latter only when specifically necessary.
Technical support of games is very often a big part of playing a game, at least on a PC. Since gamers tend to hang out in the Game Room, I figured that gave the best chance of getting the question answered.
I probably wouldn’t move a question about Windows Media Player, but a technical PC question about something like guitar tuning software would likely end up in Cafe Society.
If you have any more questions, feel free to send me a PM or start a thread in ATMB.