My first idea was that it is a game search engine. However, it is cluttered with Android apps and Google additionally advertises looking for more Android apps there. On the other hand, searching for google.books, I am redirected to google.play to buy them. So, Google Play is an online shop for everything. Which is right? Which infromation should I look for in Google Play? Can you filter the apps by supported OS? Can I filter away the ubiquitous Android games looking only for desktop games?
Google Play is Google's online shop for Android apps, music, movies & TV shows, e-books and e-magazines, and some Google devices.
Not for everything. Certainly not for desktop software.
See also: Introduction to Google Play
Let me see if I can clarify.
Google Play is where you...
They don't sell anything else there, and I would expect any expansions to be along the same lines. You can download your music DRM-free, but the other media (books, movies, magazines) are locked to the service.
In other words, it's for Google products, or content for Google products.