The problem with moving games (or any other software for that matter) is that they don't always put their stuff neatly in one folder with subfolders under them. For example many games install to C:\Program Files\ but they put their saved games under your Documents\My Games\ folder... some even put them in Documents\AppData\Local\, I caught a few which wrote stuff in the C:\ root folder, MFusion (?) put its config in C:\Windows\, etc.
Since what is important to you are usually just your game configuration and save files, it's often safest to just make a copy of those and then uninstall-reinstall the game to where you want it. Safest, not fastest.
Sure, most of the time you could simply do a brute force cut-paste + corresponding registry edits + corresponding config files edits, and it would work. Maybe 75% of the time. It's the 25% of the time when it doesn't work and you're stuck with something you can't uninstall, won't reinstall, and won't work anymore that's the problem. Especially in this day and age of intrusive DRM. "What are you messing around with the game folders for? Hmm, must be... a pie rat!" *system locks up, computer explodes, user posts angry rant on reddit*.
Jokes aside, you really want to use the "official" uninstall / install feature. After all you still have the game disc (right?), just need to backup your save files. After you're done installing to the new location paste the saves back. Usually the game's official forum (or any large gaming forum) will have game-specific advice on where exactly to put them.