UNIX is not a product (although such trademark exists) it is rather a concept or design technology.

Different UNIX flavors have made different design choices and except where there are specific emulation layers/APIs involved they are no application compatible. They are not even source code compatible.
For example, you cannot run an MacOS application on any Linux version, although both are "UNIX",simply because the neccesary API to run the application does not exist in Linux.
Another example: You can run most Linux software in FreeBSD, because FreeBSD has Linux compatibility API.

I agree with you otherwise, but the problem is that Google has made false claims. Those claims promise that any Android device will run any Android application (as long as the API level is sufficient) -- which is not exactly happening. I can see how in the not very distant future, many applications might become even more incompatible, because they were designed for vastly different form-factor and resolution.

Android applications of course can be made compatible and all this avoided, but at a cost. Google will have to adopt the Apple model for software development, where no application that goes public can avoid using the official APIs and that the OS will have to take over application behavior -- as this will provide both consistent UI and responsiveness.