What is it about OpenMosix that supports multi-process applications?

I read that 'Any single program that can run as multiple processes can benefit from OpenMosix: "The GIMP" photo editor and the "kandel" fractal generator are known to do this.

Are there other load-balancing clusters that do support multi-process applications?

Afaik not. Intrest in such technologies has rapidly declined with the availability of cheap multicore processors. Depending on your task grid/cloud technologies might be an option.