Assuming we are talking about the desktop, you can run whatever you’d like. The App Store is just one avenue for software distribution on the Mac. The situation is of course different on iOS.
Sorry, I thought the question was a critique of macOS, not the Pixelbook, and I offered a clarification that macOS is actually pretty open and you can run whatever app you like, in most cases.
For the moment. You also can't run any of the iOS apps (an advertised feature of macOS on M1) if you disable SIP, so this isn't really a true statement logically speaking.