Big Picture is of course Valve's update to Steam so that PCs support being connected to TVs, as they make it easy to play your PC games and use Steam through just a controller.
Of course that would mean Portal 2 on PC through Big Picture is just like the console versions, minus the technical drawbacks; hence why split-screen co-op is now in.
To activate the split-screen the second controller needs to 'press X' inside the first co-op menu, reveals Valve.