It's bad that Sencha is yet to reply on this here, but I am now running the 32 bit version on my 64 bit Kubuntu just fine.
This was posted in the wrong forum. (Hence why it was missed.) Sencha Architect 2.2 has additional support in this department. Could those of you having problems please post what distro you are using and the architecture?
Could you also please let us know if there is anything output to the console when running it?
This is an issue that will be short lived since Architect 2.2 will not have Qt as a dependency. To ensure the problem no longer occurs and to widen our sights on Linux compatibility, we'd love to know everyone's distro + version of Linux and Desktop/Window manager they use and we can validate compatibility.