I've bought a few games (Civ 5, Roller Coaster) on the App Store on my Macbook, but the screen is broken, so I bought a Lenovo instead. My question is, can I play those games on my new PC?
Games purchased on the App Store are for MacOS only. Purchasing these games generally gets you a license for that specific compilation / port of that game (as in many cases, it is outsourced to another company to port to Mac, they get an amount of money for sold copies).
Steam generally offers the ability to purchase once and receive every available platform (of Windows / Mac / SteamOS / Linux), but that's the exception - not the rule. The App Store has no reason to offer a similar thing for PC games.
However: If you have a game that has a CD key, and you can access the key, you may be able to use PC installation media to install the games and activate them with the key. This will vary by game, however.