Why is this power adapter transformerless?
The power supply you've found in this device is of a type known as a capacitive dropper. (More information in the Wikipedia article "Capacitive power supply".)

The primary reason why you don't see this type of power supply often is simple: it is unsafe. This is because one leg of the AC power supply must, by necessity, be connected directly to the circuit. Ideally this should be the neutral leg, but it is difficult to guarantee this -- badly wired outlets, or non-polarized plugs, may result in part of the circuit being energized by the hot leg of the AC supply.