How do the cassette tape adapters get their energy
Standard cassette tape adapters have no active circuitry. The audio signal is simply wired directly to the tape head, like this...



Your image shows an adapter which has been hacked to include the circuit from a Bluetooth stereo headset. It is described here...

How to Hack Your Car's Cassette Deck into a Wireless Bluetooth Music Player   

There is no harvesting involved. A small Lipo battery is probably hiding under the pcb, similar to this...