I think part of a useful line between “game” and “not game” whether the player can make decisions that influence the outcome.

Candyland, chutes and ladders, Life. All games, all have no player agency (Life does have one decision iirc).

At a slightly-less-elementary level: Monopoly. Lots of decisions, but a lot of them are kinda "fake" - very rarely do you want to decline to buy that property you just landed on. And the game is often effectively over even before any trading or such. The pattern is little more than "land on the right spots, don't land on the wrong spots have other people land on the wrong spots, win."

Games with fewer meaningful choices and less exploitable patterns tend to be games that game enthusiasts move away from pretty quickly.

But they stay interesting as casual diversions or ways to spend time with kids for people who are less-game-oriented.

So I think there's two types of ways games are fun, and the latter one is simply "something to do together with friends and family" where the game itself is a diversion, not the primary enjoyment source.

I was also going to add monopoly, but wanted to avoid the potential of dispute. Even though really monopoly is just rolling dice.

Monopoly is an excellent example!

And outlined features probably align to the original creative intent of demonstrating "monopolies suck and are unfair."

If you think about it... lack thereof probably being why it's still such a popular game.

Yes! I don’t think the addition of graphics makes an rng a game in any meaningful sense, despite what Milton Bradley says on the box. Maybe an activity?

Monopoly I think doesn’t quite fit with those others. Seems to me there’s a difference between the optimal choice being too obvious (monopoly) and no choice at all except whether to pull the lever again or walk away with whatever shred of your dignity remains (Candyland, slots)