Actually the Ouya doesn't run Linux as most people think of it, it runs Android. Android runs on the Linux kernel, but that doesn't mean it will automatically run native Linux apps. Steam has also announced their Steambox, which will run Linux, which is probably why they've ported the Linux platform over to steam. Even if the Steam environment were compiled for ARM architectures by Valve it doesn't mean that your library of steam games would work on your Tegra device. The games on steam are developed for a, far more powerful, desktop x86/x64 architecture.
Nvidia Shield is not running Steam, but runs a cloud computing service from Nvidia called Grid. Any android device, including Ouya, will be able to run this service and play PC games, but only through a high speed internet connection. Even then the actual computations are running on Nvidia's servers and not the Tegra device.