Oh, by reading this again, I think I know what get you confused: the input field doesn't tell vue to apply a gamma of 2.2 to the picture, but it tells the render engine: "my friend, the picture I feed you with HAS a gamma of 2.2". When the render engine receive this information, it apply a gamma of 0.4545... to "linearize" your image (sorry, this word doesn't exist but what I mean is to move the picture from the srgb color space to the linear space needed by the render engine).

So, I know why it can be confusing now :)

Input = inform the render engine about the existing gamma of the texture map so it can move it to its linear workspace
Output = tell it to produce an image with the gamma you choose burnt into the render.