It's not possible to run PC Linux games on GCW Zero without recompiling them.
The fact that both PC and GCW Zero run a Linux kernel doesn't make them binary compatible. PCs usually use x86 cpu architecture, while GCW Zero uses MIPS cpu architecture.
In order for a game binary to run on GCW Zero, it has to be compiled for: matching CPU architecture, matching OS, matching library set. Almost always this means a need for recompilation of the binary from the source code and no PC Linux game can work on the GCW Zero in its verbatim form.