I would pick one nit with the history though, CRT computer terminals were absolutely considered a "whole screen" output device. This was because IBM had made the 3270 terminal which you could download a form to, the operator could fill it out (without any computer involvement) and then hit 'submit' and have a single transaction get sent to the mainframe.
Yes, there were a few "dumb" terminals that were simply paperless teletypes, but the majority had some level of 'forms' capability which involved cursor addressing, different character highlights (blinking/underling/bold), and usually some basic box drawing characters. All in the service of allowing a 'fill-in' form that someone could be trained on quickly without having to explain "computers" to them at all. When the computer started up, the terminals would light up showing a form.
In terms of the tree of life for games, I put rogue, Walter Bright's empire, and Civilization (also called empire in some cases) as the roots for so many video games in the game industry.