The manual is not clear on this.
Basically, g is some linear combination of the R,G,B channels, the exact combination depending on which working color space you are using.
The J_z is a luminance value that is not linear, but rather is perceptual and designed to cope with wide dynamic ranges (the maths is not too difficult, so if you want to look up J_{z}a_{z}b_{z} colorspace you’ll be able to see exactly how the RGB values are mapped).