Ah, I thought the Unity standalone would run for any OS. Sorry for the mistake there, I'm going to publish up a Linux version in just a moment. Thanks for pointing that out!
It will build for any OS or Linux distribution but you have to have it selected in the project and to specify for 32-bit (default) or 64-bit (x86_64). Take your time, it's better to have a well written and thought out application across all operating systems, including Linux distributions.
I have many distributions but I focus on Debian and Ubuntu (a fork / branch of Debian) because that is where my client base has been centered.