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.
We're guessing that 5 clicks on the side button will activate Emergency SOS, but adding more click gestures for things such as Accessibility Shortcuts like the Magnifier 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.
To reiterate, to power down the iPhone X, you would 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. 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.