I would venture that a good number of games on Steam target DirectX rather than OpenGL, which means they would also need a rewrite for Linux.

Another option for Valve to explore would be to check the current state of the DX games in Wine and work with interested publishers on improved compatibility. Then throw money and developers at Wine. When they're happy, wrap it up in the Steam client somehow so its seamless for the user and problem solved. The only real issue would be the spector that MS might figure out some way to sue if it gets too popular.

Isn't WINE just an implementation of Win32 APIs? From that respect, wouldn't the recent Google-Oracle case preclude that from being an avenue for lawsuit?

That would exempt them from copyright but their's still the question of can MS dig through their patent trove and contrive some kind of violation.