How to run Android application on Windows?

You cannot download apps from the Android Market website. You can only select apps to be installed on a device that has recently used the Market app, using the same Google account that you are logged into the website with.

I recomend using the Android emulator rather than the Android-x86 project. Regardless, neither has the Market, but apps can be installed from other sources. This answer on Android Enthusiasts links to some information on that, and the Android x86 project also has info on installing apps.