I'm just guessing based on the DOCS page, but I assume that ThemeFrame is just PHP code, and will also install and run fine under Apache/PHP5 on GNU/Linux systems. (I already have my Wordpress Blog running on such a system so support is not a requirement or an issue with me).
I would suspect there are no issues on Linux to worry about, but then again there could be architecture specific binaries or something like that to muck things up? It would be helpful if the bytesforall.com website were a little more specific about Linux. It certainly requires detailed knowledge a person at the pre-sales stage would not have a prayer of knowing.