On 32 Bit Intel or AMD Systems with a recent browser and flash player installed, the program should run without problems. The same is true for the 32-Bit-(i686) version of Firefox with 32-bit plugins components.
For instance, the software runs smoothly on openSUSE 10.3, Intel Core2 (x86_64), Firefox 3.0, (i686, 32-Bit), Flash 9.0 r124.
If the Demo version runs well on your linux system, so should the full version, because both are using almost exactly the same source code.
Our advice for Linux users: Test the free demo version first, then order the full version.