The basis of depth in a game isn’t how complex it is, it is the means by which those complexities interact. The interplay between elements.
This is highly related to our concepts of dimensions. Spatial dimensions overlap and envelope each over and creates depth between them. Even our language mirrors this thought process, such as saying a character is two dimensional, flat or a narrative is deep. Depth as a narrative term comes from the literal meaning of the word depth.
Depth in games should be about adding new layers to games, new means by which the player must interpret them to succeed.
The most basic demonstration possible is to imagine a 1d game, a game where you are on a line. In a game such as this, if you encounter an obstacle. You have no real way to go around it, only through it. Collisions occur when your position is the same as another object.
Now imagine that there are two of these lines, one vertical and one horizontal, and they both operate independently on this principle. This is an added complexity, but it is not really depth. Now imagine that collisions only occur when your position is the same as objects on both axises. Beyond that, that whenever you shift on one axis, the other changes. In accordance with the shift, the prior object is no longer in your way. This is now effectively a 2d game, it has another dimension added to it. It is now possible to go around objects instead of going through them. This could be represented as a flat picture now instead of just 2 lines. But then, how do you get around objects which do not have an opening somewhere for you to go through?
Imagine there being a third line, and objects on that line can only be collided with if you are in the same position as them. Then, you can tie that into the prior two lines, and bind them all together, creating three dimensional space.
Beyond this, imagine that there were another dimension, and that analogous to the prior ones, as you moved through this dimension, objects in the other dimensions seem to shift around you. One such dimension already exists, and it’s time. The difference between time and other dimensions is that it cannot be seen, as our methods of seeing are themselves subject to time, and that collisions cannot occur with time, time passes whether we want it to or not.
Imagine another such dimension, it’s a bit hard to think about, because we don’t actually have another spatial dimension. Imagine that as you travel through this dimension, space and objects around you warp and change. One obvious metaphor for this could be color or temperature. Imagine that you could only see objects if they were the same temperature or color as you, and that you could only collide with them if you were the same color or temperature as them.
Perhaps this idea could itself be used as the basis of a game?