The MIDI specification itself does not define the exact response to the volume controller.
Nowadays, there is almost no device that does no implement the expression controller. Both the GM Level 1 Developer Guidelines and the DLS specification use L(dB) = 40 log (volume × expression / 127²). Furthermore, the guidelines mention that
there was general agreement about how these two controllers interacted
as well: In 9 cases, their values were combined (multiplied) to get the actual level. The
recommended volume response curves for CC#7 (volume) and CC#11 (expression) used
herein were provided to the General MIDI Working Group of the IASIG/MMA by
Yamaha Corporation. Roland uses the same response curve, and other Japanese
manufacturers who are members of the AMEI have agreed to do the same.
So this is how almost all devices actually implement it.
While the controller value happens to be the raw channel gain, the way it's usually measured is in decibel, and that is a logarithmic scale. That the internal channel gain is not measured in dB is of interest only for somebody who actually builds a synthesizer.
(And the way how the human ear perceives the volume is proportional to neither the raw gain nor to the dB value.)