I'm not at all familiar with the Xbox One, but this is a feature that's generally available if you're designing "closed" hardware like a console. Most SoC these days have some sort of security processor that runs in its own little sandbox and can monitor different things that suggest tampering (e.g. temperatures, rail voltages, discrete tamper I/O) and take a corrective action. That might be as simple as resetting the chip, but often you can do more dramatic things like wiping security keys.
But this exploit shows that it's still almost impossible to protect yourself from motivated attackers with local access. All of that security stuff needs to get initialized by code that the SoC vendor puts in ROM, and if there's an exploit in that, you're hooped.