Is "Inbox" the old stock email application? I am setting up a new Nexus 5X with Marshmallow. There does not appear to be a default mail application as in prior versions; instead there is just the GMail application. Is the Inbox by Google application what was formerly the stock mail application called "Email"?
No. Inbox is a very different application that was opened to the public in early 2015. It's primarily designed around the idea that your inbox is like a to-do list of sorts. The project's website explains this in more detail.

The "Android" email application is no longer developed by Google in any meaningful capacity, aside from ensuring that new platform releases do not break the build (and some translation updates, which are mostly automated). The Exchange and IMAP/POP features were instead rolled into Gmail, which is now considered the "stock" email application on any Google device.