If the question is about tiled isometric-view video games (see https://en.wikipedia.org/wiki/Isometric_projection and https://en.wikipedia.org/wiki/Tile-based_video_game), then it's a less meaningful question because isometric games tend to have a huge number of simplifying assumptions built into them. First, the game typically doesn't have a "projection" as such, because the game system is based on a square grid and covers such a small and abstract area that spherical distortion never comes into play. The game designer will typically assign the notion of "north / south / east / west" to either "grid up / grid down / grid left / grid right" or "screen up / screen down / screen left / screen right" or some other variation on grid coordinates / screen coordinates (grid coordinates will often end up with north at 45 degrees up and right or 45 degrees up and left, while screen coordinates often go with north being up). Using one of the game grid axes as "north" simplifies discussion in terms of keypresses mapping to the cardinal directions. Using screen directions as "north" keeps the familiar concepts for the user.

The above information relates to the classic games that are grid-based and units can only occupy one grid space because the game's implementation is more or less "units must occupy one grid space because we have one byte of memory to store one grid space and it has to index into one of our 256 different sprites". More modern third-person-perspective games based on fully 3D engines allow rotation around the in-world "up" axis and may dispense with the grid (partially or entirely), but might keep the isometric diamond shape onscreen purely for nostalgia reasons.

One thing to note above is that I keep harping on the idea of in-game world space "grid space" as being distinct from "screen space". That's a really important distinction because the abstract notion of "North" on the displayed screen will be whatever is convenient for the game developer. If you start with a simple tile-based game, you are starting from a rectangular grid. Using rectangular tiles for display of a piece of the game world gets you a rectangular section of the screen. Using diamond-shaped isometric tiles of the exact same piece of the game world gets you a diamond-shaped section of the screen. Either of those raw displays can be clipped to an arbitrary boundary, but just keeping the simplest-possible display will get you specific shapes.

I hope that made some sense, anyhow.