I am not sure this is the solution, but you could call "ldd <file>" on a unity generated binary to see system dependencies. If they statically compile stuff into the game, that's another question.
linux-gate libdl libpthread librt libGLU libGL libX11 libXcursor libstdc++ libm libgcc_s libc libnvidia-tls libnvidia-glcore libXext libxcb libXrender libXfixes libXau libXdmcp
I know that steam has some 32Bit dependencies even on a 64Bit OS. I thought it might have only been the steam client's dependency. Unless you're using a 32Bit OS, it seems that Steam, or maybe even Unity3D, enforces the use of those 32Bit libs.
I wonder why.
Edit: I seems that you removed the references to lib32 and i386.
Between those two, I've probably sunk whole weeks of my lifetime. If someone were to make a game that combined the two into some kind of orbital city builder, I'd be set.