Somewhat related, I noticed that the Nimatron Wikipedia page [1], which has quite a bit of interesting info, also mentions Nimrod.
On its Wikipedia page [2], it says, "The Nimrod, built in the United Kingdom by Ferranti for the 1951 Festival of Britain, was an early computer custom-built to play Nim, inspired by the earlier Nimatron. The twelve-by-nine-by-five-foot (3.7-by-2.7-by-1.5-meter) computer, designed by John Makepeace Bennett and built by engineer Raymond Stuart-Williams, allowed exhibition attendees to play a game of Nim against an artificial intelligence."
Also an interesting read, in my opinion at least.
These handhelds LCDs that could only display a small number of images are also considered video games.
I didn't consider them video games growing up. It's going to vary from person to person.
For example in the 1980s I owned a hand-held electronic interactive game made by Tiger, called John Elway's Quarterback [1]. They try to call it a video game on the back of the packge it was sold in (an "LCD video game"), but back then (~1989) Nintendo games were video games, and that Tiger device was merely an interactive electronic toy game (as far as I was concerned). GameGear was a video game however, as was GameBoy (video game playing devices; the cartridges were the video games, to be specific); I think it's the depth/elaborateness of the game (what it's capable of) and level of interactivity possible that separates them in my view.
[1] photo from eBay: https://i.imgur.com/PVcMFok.jpg