Tightcircuit, Indonesian CASR part 91.175 (c) (3) does require the runway, approach lights or threshold markings to be in sight before descending below the MDA. Since there are no approach lights leading to runway 09 at Denpasar, then the crew would need to at least have the threshold or runway end lights in sight to continue below MDA. To say that you do not need to have the runway in sight in this case is wrong.
If you did have it in sight, of course you could continue the approach. Noone is arguing against that (or else you would never ever land), but, as stated in the Indonesian CASR part 91.175 (e) a missed approach must be conducted at any time you lose sight of the runway when below MDA.
Even if the captain had sight of the runway at MDA, he definitely lost sight of it later on. And I suggest you re-read the report. The FO stated twice that he could not see the runway. It was only the captain who 'claimed' to have the runway in sight which he obviously didn't because the inbound course of the VOR is 091, but the runway track is 087. There is a 4 degree offset which must be corrected for when becoming visual to line up with the runway centreline. The data from the report indicated the aircraft continued on a track of 091 until it hit the water. The captain obviously wasn't visual at the MDA.