The Nvidia Shield is the most powerful streaming TV set-top box ever made. With it, you can stream 4K videos and play console-quality videogames, two things you can’t do on a Roku, an Apple TV, Amazon’s Fire TV and even Google's’s own Nexus Player.

It can do all this because the Shield isn’t just any old video box. On the outside, it looks like a stealth bomber. On the inside, it has Nvidia’s beastly Tegra X1 chipset, with a 256-core graphics processor and 3 GB of RAM. With all that power—and an Xbox-style controller that...