If I compile a desktop app (desktopApp:build) it will be only built for the current platform, or? I.e. under a 64bit Linux I will get a 64bit linux binary, right?

It depends what platform this desktop app targets. Is this a JVM app? If this is the case, JVM bytecode isn't platform-specific. If this desktop app is a native target and the build script is creating the target based on the host system platform, then yes, that's the platform that would be built. It depends on your build script.

Ah. I think I might not have configured native builds then. Eh, confusing.

If you can share your build script and provide more info about what you're trying to do, we could assist better.