You don't need to use Express for Angular. You could use another framework or just the plain node.js core http/https server directly. Express just incorporates abstractions and conventions on top of the built-in node.js http/https server to make it easier to write your backend logic.
See wikipedia for both a good overview of what a template engine is and a list of example template engines.
Template engines aren't necessary to generate output, but they can certainly aid you in that process by making it easier/simpler to compose output, instead of manually concatenating or echoing a bunch of strings for example. PHP kind of has a "template" built-in, in that output buffering is used such that you can just inject <?php ?>
blocks anywhere in the output. This is similar to many template engines, including ejs, except ejs can save the template as a reusable function instead of throwing it all away once the request is done).