One click on the iPhone X's Side button locks or wakes the device. Two clicks opens Apple Pay. Holding down activates Siri. So how do you shut down the iPhone X then? On every other iPhone, you hold the Side button down until the "slide to power off" option appears, but that doesn't exist on the iPhone X.
Five clicks on the Side button will activate Emergency SOS, but adding more click gestures for things such as Accessibility Shortcuts like the Magnifier (which is 3 clicks) will make things complicated and too easy to accidentally activate.
All of this explains how the new "Shut Down" button in Settings –> General got there in iOS 11. It seemed like a good option for people who had a broken sleep/wake (aka power) button, but now it seems especially fit to shut down the iPhone X, which just has the Side button now. But that's not the only way to shut down the iPhone X.
Since Siri is now activated by pressing and holding the Side button, there's a new way to power off the iPhone X with buttons. Just squeeze (i.e., long-press) the Side button and either Volume button together at the same time, and hold them for a few seconds. You'll then see the "slide to power off" option appear on your screen, just like on other iPhones.
Note: If you quickly squeeze and release the Volume up and Side button without holding, it'll take a screenshot instead of showing you the power-off slider.
If you don't like those button presses, you could open up the Settings app, tap "General," then scroll down to the bottom and tap on "Shut Down" to bring up the "slide to power off" option.
Once you've turned off the iPhone X, to turn it back on, you would just press and hold the Side button for a few seconds. Alternatively, you could plug in a Lightning cable to charge it, which will also turn the iPhone X back on.
But there's another way — using AssistiveTouch. There's an option to "Restart" right in the AssistiveTouch menu, a new feature in iOS 11, so if you just want a quick restart, this is the fastest way to do it, as long as you assign AssistiveTouch to the triple-click Side button shortcut.
So, that's how you would restart the iPhone X. From what we can tell right now, Siri won't be able to shut down or restart the iPhone X, just like it can't on any other iPhone model.