Check the two black electrolytic caps on the left in your first picture. Are they rated for about 400 - 450 volts?
If so, what you have is an input rectifier which will produce a high DC voltage at the caps. The transformer is then part of a switch-mode power supply which is effectively a DC-DC converter which converts high voltage to low. Also known as a buck converter.
Something you'll need to learn about transformers is that the higher the operating frequency the smaller the transformer needs to be for a given power level. So, as Michael Karas answered, the transformer will operate at about 200 kHz rather than 50-60 Hz,and can be much smaller than a transformer which operates at line frequency.
And why 200 kHz, you ask? It's part of a compromise. While increasing the switching frequency reduces the size of the magnetics, it also increases the power dissipated in the switching device, usually a MOSFET. So, depending on the exact circuit and construction, switching power supplies usually run at about 100 kHz (more or less), where the value of the continued shrinkage will be outweighed by the increased power dissipation of the switch. The exact frequency will depend on exactly what circuit is used, what components are selected, what voltage/current combination is specified, the temperature limits on the circuit, emitted RFI issues, and a bunch of other considerations.