Why is my two way dimmer switch not working?
The dimmer switch has some solid-state electronics in the path between the electrical mains and the light that it controls: definitely some form of transistor, and most likely one or more MOSFETs.  MOSFETs have very high resistance when they're off, well into the gigaohm range (or higher), and very low resistance when on, in the range of 1 ohm (or lower).  Other transistors types have a less extreme swing between on- and off-resistance.

The rest of the circuitry in the dimmer is designed to operate on AC mains voltages, so the small DC voltage that your multimeter drives through the dimmer isn't enough to turn on any of the transistors in the conduction path, so you're reading it as being open-circuit.