The key insight is in the patent: "The transmitting electrodes are powered with A.C. voltage in such a way that an electrical rotary field forms which generates A.C. voltages on the receiving electrodes, and the phase position from the transmitting signal to the receiving signal is proportional to the displacement between the stationary part and the displaceable part of the transducer" It's not necessary to measure capacitance directly. Just phase angle. Which has the nice property that, as you move from one section of the comb to another, you're not going to get a jump. It's inherently monotonic.
This is how a resolver[1] type encoder works. It's a rotary transformer with two stator phases at 90 degrees forming a sine and cosine output. The rotor has an AC current passed through, usually a few kHz, and the phase angle of the outputs vs the input is directly related to the shaft angle. There also exists a linear version called an Inductosyn which is similar to the calipers capacitive scale.
They are absolute for a single rotation meaning if power is lost and reapplied, you still know the angle of the shaft (good for robot arms). This absolute positioning is not possible with a quadrature encoder.
you can turn capacitance into a waveform pretty easily, thats what the 555 timer does effectively, measure the time it takes to fill a capacitor. (https://en.wikipedia.org/wiki/555_timer_IC its analogue.)
