I bought a game on Windows — can I play it on my Mac?

A paid game is bought per platform. Buying the Windows version entitles you to Windows; playing the same game on macOS is a separate purchase, and the launcher on the other machine will show it as available to buy rather than installed.

Two exceptions:

• Free games are granted for every platform the game supports.
• Older purchases, made before per-platform licences existed, cover every platform and are not affected.

In a browser your library shows everything you own on any platform, which is why a game can appear there and still ask to be bought inside the launcher on a particular machine.