How does multimeter AC measurement work?
First, I'll note an erroneous assumption: AC meters do not display peak voltage but rather RMS voltage. This is a sort of "average" voltage that makes all the math work out right.

Now, to answer the question:

There are two main methods of doing AC measurement: the cheap way, and the accurate way.

The cheap way is indeed how you suspect: rectify it and measure the peaks, and then divide by √2 to get the RMS. This works only for sinusoids, because the factor of √2 implicitly assumed a sinusoidal signal.

The accurate way uses what's called a "true RMS converter", which is a circuit (analog in older true RMS meters, probably digital in modern ones but don't quote me on that) that actually calculates the RMS voltage with appropriate signal processing techniques.