It is not a video game because there's no video. But the idea is cool and a good representation of the state of art in commuting circuits at that time.
I prefer selecting "first" in terms of context/influence. Unless Bushnell, just to pick an oft-named starting point, was not inspired by (or even heard of?) the Nimatron then Nolan might be said to have won round one against Nimatron.
I think what's interesting is the direct lineage leading us to, say, Pac Man — not just who checks off the minimal definition of "video game". But as James Burke showed us, working backwards can take us in all manner of strange directions so it is not an easy task.