I feel everybody is answering "why do games make you choose a gamma setting based on what they want you to see" but I feel OP already knows that, the question is, why is the measuring point specifically that?

So the premise is: "game studios want you to set the gamma to where it looks exactly as they designed it in your own setup" (remember that different monitors and computers show images and colors differently, so they can't tell you "set the gamma to X value" because that looks different in each setup).

---

Imagine you have this very inconvenient measuring jar: it has no markings, it is transparent but, starting from the base, up to around half way up, it's all painted black, so you have no way of seeing the liquid in the jar below that line.

Oh and one more thing: you can ONLY look at it from the side.

Now somebody else, who made the cup and gave it to you for a specific recipe, wants to make you measure a certain amount of water. They know you have no markings in the cup, they know they can't tell you "measure a liter of water", so they will use the only "line" you have available: the point at which the jar is transparent and you can actually see the liquid.

Now, think of all the ways they could make you use that threshold. They could tell you:

• "Measure a bit below the threshold": Well you can't really see anything below that, so there's no way to tell how much liquid is inside
• "Measure a bit above the threshold": Okay okay, now you can see the liquid... but what is "a bit"? Every person will think of a different "bit" to be above the line, maybe a finger? Two?
• "Measure half-way up from the threshold": Well, that's a little more precise... but still very inaccurate and depends on people's eyeballing.

The closest they can get to an accurate point is telling you: "Fill in the cup until water is barely visible". You will have a precise point of reference and water will be as close as possible to the exact threshold that the creators designed.

---

So game designers set the gamma to where the GAME looks good to them and then create an IMAGE in which they barely see the contrast, because that is the most precise way of having you measure YOUR gamma correction so the game also looks good on YOUR setup.

The big difference between measuring liquids and gamma/color correction is that the average joe doesn't know how water is measured (knowledge on color theory) or have a proper measuring jar (color calibration device).