called a video game, but I feel like that’s for lack of a better term

Its the perfect term for it, your definition of “game” is likely incomplete:

A game is a structured type of play, usually undertaken for entertainment or fun, and sometimes used as an educational tool

Note that it’s usually for fun, but does not need to be. Flower is a game by that definition

Adding “video” to it is probably the weaker part of the phrase, “digital” is probably more accurate but I doubt people are going to change terminology like that for something so minor