This is real electronics porn. Simply speaking RFID tag is built by using AVR Attiny85 and small inductor. The power pins of AVR aren’t connected at all. It works, but how?
Secret lies behind nature of IO/O pins of AVR. Coil connected to input pins power chip itself via clamping diodes. Once power problem is solved there is one more – chip clocking. Because voltage is too low to start chip internal oscillator. So coil also is an external clock source. This is why it has to be connected to AVR clock input. As RFID frequency is 125kHz so the AVR is also clocked at this rate. Firmware also has to perform on edge of resources.
Probably to have reliable operation you would add couple capacitors and bigger coil. In other hand this is great hack showing how low can AVR go.