Output resistance of an amplifier
To calculate the Thevenin equivalent circuit, you set voltage sources to zero (e.g., make voltage sources shorts) and calculate the impedance between the nodes with no load. That's all that's happening here. It's just explicitly showing that the dependent voltage source is also zero (a short). That means the output impedance us whatever /$R_0/$ is.
In the PDF, they also describe how you can use that to measure the output impedance  as Tony Stewart points out in the comment.