Following the instructions within the plugin (printed onscreen when you install the plugin) prints the shortcode to the screen. The install instructions here on Wordpress.org is correct, but not within the plugin itself. I discovered that the shortcode needed to be changed [amp_related_posts]. I presume the plugin was renamed at some point.
Despite this fix, there were a few issues:
There's still an error printed to the screen. Something about expecting a 4th param.
The plugin ignored any settings added to the plugin settings interface. There was no featured image and the plugin printed 5 related posts instead of the 3 I set it to.
I'm not going to spend my time trying to resolve the issues. It needs a little work before it's ready for prime-time. For now I'll look for another solution.