I ordered two and both were either broken or (more likely) different chips with the ym2612 markings put on. When I powered them up, even with only pull-up resistors on all pins, they get extremely hot within seconds.
Apparently I was at fault for the chips burning out. Since the datasheet for this chip is in Japanese (and I don't fancy trying to decipher 132 pages in a language I don't understand), I didn't realise that the audio output pins need a pull up resistor of 2.2k. If it's not connected, the DAC inside will overheat and your chip will be damaged if not ruined.