How does this high amperage LED dimmer work while being so small?
For sure it's using PWM to control the lights via a MOSFET. 

A tiny SMT MOSFET can easily control a few amperes at 24V and remain very cool. The controller chip is probably an ASIC or a microcontroller, given the up-down button control scheme. It might take 10 or 15 components total including the power supply for the controller.