The luminance we're talking about is not the overall luminance, but the luminance of each color component in R, G, and B. Note, though, for a strictly gray-scale image those are the same thing and most explanations of GC try to demo it with shades of gray.

Your screen pixels comprise three components. In each pixel, one is red, one is blue, and one is green. The color you percieve for that pixel is controlled by the amount of red luminance, green luminance, and blue luminance, combined. The luminance is controlled by the voltage applied. The voltage is controlled by the numbers we store in each pixel component. The ratios of these RGB luminances within a pixel give rise to various hues and saturations.

GC is applied in order to produce the R, G, and B luminance calculated by our shaders/lighting model. Without GC, the intended luminance of each pixel is not actually produced - something darker is in all three components. Therefore the overall luminance is darker. But also, the overall hue and saturation is incorrect as well.

GC is directly about mis-represented luminance.

Mis-representations of luminance also produce mis-representations of hue and saturation.

Therefore, indirectly, GC is about hue and saturation as well.

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