How to display a twig template via a controller's render array
The problem turns out to be a missing ' mark in the twig file itself.

It turns out that the twig was rendering, but since I had

&lt;div class='examples-description&gt;


and not

&lt;div class='examples-description'&gt;


the browser refused to show the badly written HTML. 

So this was user error, but a hard user error to debug.  I saw what was going on by looking at the source for the page, which made it obvious.

Hopefully this will save folks some trouble.  But in any event: the technique I use here is valid, and works if you don't do stupid things in your twig :-)