What likely caused this drive to catch fire?
Very difficult to say. Something bad happened in the vicinity of that connector, but was it the cause or was it an effect? A high current was drawn, but that was presumably an effect of something else.
I'd guess power surge (on the electricity supply) would be unlikely, because whatever happened continued for a matter of quite a few seconds and not milliseconds or microseconds. On the other hand, if the power surge killed the power supply (should be unlikely, but some power supplies are, err, not very good) the power supply might deliver a high voltage (...should be unlikely...) for an extended period.
A power supply blow up is possible, but there might be some evidence in the power supply (but, you'd have difficulty telling cause from effect).
A bad connection in the cable, which would probably have to be a short between something like a short between one of the power supply lines and ground, and the short in either the cable side of the connector or the board-mounted side, would be possible, and should leave some evidence (ie, a fragment of copper that formed the short, or a trail of blackened material).
It is possible that an internal short in the hard drive could cause this kind of fault. It would probably have to be a short between a power supply connection and something else (eg, ground) for enough current to flow to cause this kind of damage.
I did look at the two darkened areas and wondered whether there were tracks on the other side of the board, or internal to the board, that could carry a high current, but I doubt that's right (that would probably be clear if you look at the other side of the board) - it probably is the connector itself, at those two pins, which overheated and which blew out some rubbish and it left that evidence across the board. Looking more closely at the circuit lands/connector receptacles might give you more of a clue.
For example, a screw shorting from the chassis to a power supply track could cause that kind of thing, but evidence of that ought to be very obvious. Well, there'd be that screw, for a start.
There is also some evidence in the mark on the chassis, but it is a bit difficult for us (not for you!) to work out the alignment between the chassis marks and the former alignment of the drive and the connectors.