That's a Sony Z1 Compact; due to its waterproof design the touchscreen is a bit different. When you break the screen glass, the touchscreen seems to stop working.
However, the phone has full USB OTG support, including power delivery to devices - and it is actually shipped with that short black adapter cable in the box! (Works great with USB memory sticks, but also mice.)
So, if you really break the screen, you can make the phone usable by plugging in a mouse. I've done the exact same thing. (Though there's no photo of that.)
Of course it's still impractical :) - but if you dropped your phone and have all your contacts & social foo on it: great workaround! In fact, that person is a true hacker.