Verify 1 thing. That what you are booting is actually the new OS and not the old OS on the HDD.
When you 'install' a game, it asks for a place to install it. Sometimes this is 'Express' and chooses its own path, like C blah/program files x86/tonka/game. Most of the game files go there. Other files get opened in C user/appdata/local/mygames/tonka/ etc. The connections and links are written into the registry so when you hit the "exe" shortcut, the pc knows to load certain audio links, display drivers, make connections to the my games folder and Tonka folders etc.
When you move the hdd, physically, that's all still there. If you change the OS, it's not. Physically it is, but on another drive and not recognised. It's like if you and BFF had seperate profiles on the pc, he can't access your files, you can't access his.
The only games that will work as is are non installed games. Self contained, same as if you were loading from a dvd. You supply the shortcut, the game does the rest, not the pc nor windows. Many older games were that way, almost all DLC games are not, they tie into windows now and use the library system.
You'll know a game or app that's actually installed through windows, because when you look in tools, there's a link to 'Uninstall' the game. Same as there's a link to 'Uninstall' Steam, or Origin or U-play or nvidia files etc. Those apps have a Windows Installer data file that contains all the places and registry entries etc. When you uninstall, that data and addressing is removed and 'technically' renders the game or app unusable and available to be written over.
By swapping OS drives, the new OS doesn't contain the Windows Installer info, so 'technically' the game doesn't exist. Only self contained, non-installed games will then work.