Very interesting. The question of "first" is often tricky because definitions are often only made after something has become established and then retroactively applied to earlier creations.
This predates 1958's Tennis for Two which is often said to be the fist videogame.
Earlier candidates are 1951's Nimrod and 1950's Bertie the Brain which are both often excluded because their display consisted of lights rather than generating graphics.
As pointed out in the article, I'd opt for a definition about a visual, interactive feedback loop running in real-time and wouldn't care about the method used to display the visuals. E.g., if you were displaying Space Invaders on a neon matrix on your mainframe's control console, I'm fine with that. (This is also, why I didn't dig into the claims or the verdict of the court case.)
However, things worked out a bit different in the Magnavox lawsuits. Notably, Ralph Baer didn't understand, why lawyers would concentrate on the analog vs video side of things. To him, it was all about a principal claim about detecting object collisions between a human controlled screen object and one controlled by the machine. (Compare his view on these legal matters as in "VIDEOGAME HISTORY: A little matter of record keeping" [1].)
From this angle, there is no intersection with Michigan Pool, since the positioning of the cue stick isn't of any relevance to the program, only the angle as chosen by the knob, regardless of the on-screen position of the cue stick. So there's no collision detection involved for cuing, and when collisions are subsequently detected, these are all between machine controlled objects.
Definitions are always tough. Are text adventure games "video games?" How about games with no visuals at all like A Blind Lengend http://www.ablindlegend.com/en/home-2/
What about things like Mattel Football? When I've taught videogame courses I ask my students these questions and they often fall back on the old "I know it when I see it" rational.
Are text adventures video games? With a focus on the kind of interaction, probably not. However, it may be interesting to observe, how computer games tend to reflect the mode of HCI in general. In the days of X-Y displays and console switches (and light pens as well) – wherever those had been available –, video games may have been a more obvious option. On the other hand, exploring the parsers of text adventures and the world hidden behind them reflects perfectly the principal mode of interaction in the age of terminals and time sharing (or text consoles in general).
P.S.: Compare https://www.masswerk.at/pmd/ – ist this a video game? If so, close the map window (enter "hide map"), is it still a video game?
I also always heard Tennis for Two as the first video game, and this pool game even looks more complicated than that one due to the many balls, good to know!
Apparently, it depends on the definition. Personally (as pointed out at the beginning of this write-up), it's more about a visual feedback loop and fluid user interaction, which would exclude turn-based games or any presentation that runs autonomously while triggered on some user input, which is evaluated at the start of the program (compare Bouncing Ball or Mouse in a Maze). I guess, what makes a video game a video game is the kind of interaction – and typically a user may choose to interact or to not interact at any given iteration of the principal main loop – and this required real-time computing. There's a distinction of a "mere" computer game (whatever the output medium) and a video game. We may even add some cultural notion, like that a true video game had to introduce some "magical" world of its own (by invention or abstraction) as opposed to just recreating an existing game in faithful on-screen simulation. But, again, this is subject to debate.
For me, when it comes to digital video games (i.e. a visual real-time game running on a digital computer), the first one we do know of is still "Spacewar!" (1962).
--
Edit: The cultural argument is rather similar to the question of rejecting "doing things on a computer" in tech patents.
This predates 1958's Tennis for Two which is often said to be the fist videogame.
Earlier candidates are 1951's Nimrod and 1950's Bertie the Brain which are both often excluded because their display consisted of lights rather than generating graphics.