Since you mentioned the Store, I assume you are using Classic Shell on Windows 8/8.1. The Games folder was retained by Microsoft in that OS but all of the classic games themselves were removed. Classic Start Menu's job is to only show the Games folder, not to revive the Games.
To get back the Windows 7 games, see these articles:
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Get Windows 7 games for Windows 10 (applicable to Windows 8 as well)
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How to bring back Windows 7 classic internet games on Windows 8 You may also find Store versions of some games interesting:
40 FREE Store games for Windows 8 including new and classic ones To put back the actual games shortcuts inside the Games folder, locate the EXE of the game, right click it and click Copy. Then open the Games folder by right clicking it in the Start Menu -> Open. Right click in an empty area of the Games folder and click "Paste shortcut".