I am wondering what games are out there that don't really have geometry in the usual sense.

I know that can be said of many visual novels, where there's no way to move from one place to another, but I am curious as to what other sorts of games are out there that don't really have geometry or space.

I suppose that Cookie Clicker and similar games might qualify (note that flavor text doesn't count here).

Can you rephrase the question? Do tower defense games like Plants vs Zombies count, or does the fact that enemies are still moving towards your end of the lawn (the house) mean they have "geometry"?

Do you mean there is no movement from A to B even within the current space, not by you nor any other object or character in the game?

In a sense, I would say that I am looking for games that don't even have space in the usual sense.

For example, in Cookie Clicker, there's no space to move around in; there's a cookie that you can click, there's the occasional golden cookie (or reindeer in a specific season), and the rest of the game is just menuing; there's nothing that really moves in the traditional sense. (Incidentally, there is an old beta version that has a dungeons minigame, in which you move within the minigame (it seems to be something like a roguelike), but that's only a minigame and is not in the current live version of the game anyway.

Plants vs Zombies I'm not actually familiar with, but it looks like it might have geometry. How about this: Does the game have collision detection? If so, then it has geometry.

(Note that games like Tetris and Bejeweled can be said to have geometry in this sense.)

I'd say most business management games. The spreadsheety ones. Even those that have a map, which is just a tick-new-location thing (as opposed to business management games that are about map positionning, like city or tracks builders).

Ports of Call probably has geometry, somewhat. But i'd say Airline Tycoon doesn't. Or maybe you'd argue that the airport corridor scrolling menu is geometry...

Game designers go out of their way to use the visual space of the screen and make it relatable. Dressing up its buttons. Like any game is a dressed up series of equations. So you can always argue that there is geometry in a game made of a control panel (especially if it emulates a physical one, which most designs like to do). Now if the represented control panel is spread over a table, a room, or a building, when does 'geometry' pop in for you ? TIS-100 has no geometry but Human Resource Machine has, yet they are the same game.

Does Her have geometry, for instance ? Does Psi 5 Trading Company ? What about Stories Untold or Papers Please ?

There is a long gradient down to chatterbox games (from Racter to Sorry James)...