Ubuntu 16.04 keeps turning off the screen after 10 minutes

Your monitor is being turned off every 10 minutes because of the setting you have in:

timeout:  600    cycle:  600

The 600 seconds timeout is 10 minutes. You can disable this timeout by changing this setting to 0.

You can do this with:

$ xset s 0 s blank

I don't know what in your system is making this a default. But you can make this an automatic change by creating a script to change this and placing the script in your Startup Applications configuration:

Script to disable blanking:

#!/bin/bash

xset s 0 s blank

Copy the script to ~/bin/.

Now set it to automatically run by typing start applications in the Ubuntu Search button and clicking Startup Applications

Click the option to Add, then browse to the script and add it.