Slave labor, I'd assume. Why trash the place and any pre-existing infrastructure when you can just appropriate it?
Because an iron age society is completely worthless to a starfaring people whose primary economic sector should be almost totally automated, with naught but a few technicians to oversee it, ala
Moon. The gross domestic product of the whole planet of Organia is negligible: field after field of inefficiently raised staple crops that are, from an evolutionary standpoint, probably not even digestible, even if they turn out not to be some kind of weird energy construct and not real food at all.
Timo said:
Nitpick of the hour: that'd have been Kor.

I should've looked it up.
It's unclear what the Empire needed of Organia to begin with. Supposedly this planet was at a strategic location, but what was its value to a high-tech star empire intent on waging widespread war? Everybody thought the planet was primitive and agrarian. Would the Klingons have needed slave labor? Or would they have brought their own equipment, either agricultural or then of other, unknown nature and purpose, and provided their own workforce?
It might have had some valuable mineral resources, or simply a strategic location. Neither one of which would require keeping the Organians alive.
The second wouldn't actually require going down to the planet at all, as, taking Organia at face value, vast orbital facilities for their space fleet could be constructed without the Organians
even knowing--or, if they had good telescopes, without the Organians being able to
do anything about it. If the Klingons had established a presence in Earth orbit in the time of Galileo, maybe he could have witnessed the construction of Praxis II on our moon, but what exactly could we have done to clear them from what we would surely consider "our" cosmic real estate? Given the defenses of starships, it's actually unlikely even modern ASATs and nuclear arsenals and so forth could vacate a space fleet intent on staying, even if they were resolved to never fire a shot...
In any case, it doesn't seem that the Klingons were all that interested in defeating or subjugating the planet's inhabitants as such. Their, and the Feds', interest was in controlling the planet and preventing the opposite side from gaining it; the natives probably didn't feature much in that equation, and wouldn't have been worth the ammunition costs of bombing to submission.
Whether the Klingons would have "purged" the planet afterwards is unknown. They aren't particularly xenophobic or anything, and their prominent prison planet seems to be full of non-Klingons. They could easily be of the sort that conquers primitive planets, and then makes sure the planets stay primitive, so a rebellion there is of no consequence and reconquest is trivially easy. No need to kill the natives, then. At least not all of them.
A good point--although it's by no means assured that the aliens at Rura Penthe are Klingon subjects. They could just as easily be foreign nationals, not executed because of treaties with their respective governments... this certainly seems to be why Kirk and Bones aren't subject to capital punishment for their putative part in Gorkon's assassination.
However, you make a good point about the necessity of genociding all of Organia. Again, taking Organia at face value, to establish a planetside base (of dubious military or economic value, but let's assume it is necessary for some reason) the communications and logistics capabilities of the primitive society would make it easy to create a zone of control. Yet there did not seem to be a great need to rely on ground troops or stockpiles of flammable ammunition.
It probably would have been better to simply kill everyone in Organia's Iceland or Hawaii, and establish their base. It is impossible that the Organian society could retaliate (at least the one depicted, not the true society populated by advanced space gods). With a suitably chosen site, it is unlikely that in the near term that Organia at large would even realize there was an alien genocide in the first place. The Chinese of the 1500s were certainly quite ignorant of the depradations of the Aztecs, for example.
I wonder if Spock's presence might have mitigated the Klingons' mode of control? Been a while since I've seen "Errand," so maybe this is actually mentioned... but killing a Vulcan national, whether he was a travelling merchant or Starfleet officer or whatever, might have been more inflammatory than Kor would have easily countenanced, and letting him live while genociding a bunch of Organians might have permitted the story to get out, influencing interstellar opinion against Klingon butchery.
Alternatively, it
is possible that the Klingons, despite their bad press, particularly in the TOS era, have
moral qualms about simply massacring an unarmed populace. And even if individual decisionmakers don't really care, they may yet have fears that domestic political rivals could make hay in the Council with such pleas to morality, honor, and so forth.
I deeply believe one, the other, or a combination of moral and domestic political concerns is the only way to explain Cardassia's restraint during the occupation of Bajor; perhaps the same explains the Klingons' apparent distaste for outright genocide (Tribbles excepted).