I can't see the detail, but the LEDs are almost certainly in series. I would guess that the 8 chips are in series, totalling 72 V, so that the is 9 V on each chip. You could confirm that on a working one by measuring the voltage across one LED chip. I have seen LED chips with three separate LEDs, each wired to two terminals, so the assembly has 6 terminals. It could be that you have something like that with all three wired in series.
If the plate on the back is correct, that is 27 W in total, or 4.5 W per lamp, so that is 62.5 mA at 72 V. So you are looking for LED chips that are 9 V (3 LEDs in series) and rated at 62.5 mA (or 560 mW) or more.
It is quite likely that the chips are rated to a higher current than they are being run at, so if you find some higher-rated LEDs chips that are still 9 V, they will be fine.