Well, actually, yes it does. It measures pressure and computes and displays altitude (actually, an estimate of altitude) through it’s mechanism. An altimeter is in fact an analog mechanical computer, although that may be a little abstract for some, but it is true nonetheless.
You are correct that it is a relatively simple clockwork mechanism, you are absolutely incorrect that it changes the hands 1000 ft for every 1 in. Hg pressure change. Pull out a chart of the IACO standard atmosphere. At sea level, 1000 ft is 1.06 in Hg. The difference between 19,000 ft and 20,000 ft. is 0.59 in. Hg. That is a *LONG* way from 1 inch each and every thousand feet. Even in the idealized standard atmosphere, pressure is a non-linear function of altitude
I should probably clarify what I meant by altimeter settings being corrected for temperature. True, they don’t take a pressure reading then apply a factor to it based on temp, however an altimeter setting, by it’s nature takes into account the effects of non-standard temp. Atmospheric pressure ant any point will be affected by the pressure patterns ant temperature, and possibly other factors. So if you compute an altimeter setting for a location based on the measured atmospheric pressure at that location, the altimeter setting will account for any factor which affects the pressure, including the temperature.
What they are doing in step three is adjusting for the altitude difference between the pressure sensor and surface of the field, and that altitude correction includes a term for temp.