The Medrash Rabbah בראשית ל''א ס''ק ה says that what the people of the Dor Hamabul did in order not to have to be punished by their courts is to steal less that a Prutah (minimal Monetary Value) which Halachicly makes them not responsible to pay.The question is that Halacha only applies to Jews a Ben Noach is responsible even for less then a worth of a Prutah?
Even so, the definition of chamas, as opposed to gezel, according to Rabbi Chanina in Bereishit Rabba is less than a shava peruta. (So too Rav Acha in Yerushalmi Bava Metzia.) Since the pasuk mentioned chamas, rather than gezel, it is a midrashic approach to look at the halachic definition of a chamsan.
The courts back then, presumably, did not work according to the halacha. And so they did this in order to evade their courts, taking action just like a modern-day halachic 'chamsan'.
Although this is speculation, you are talking about a Midrash explaining why the Dor HaMabul deserved the flood. Post-Mabul Bnei Noaḥ - by definition - have different rules than the Bnei Adam who lived prior to (and were punished by) the Mabul. Prior to the Mabul, perhaps, their courts had a Perutah requirement - or perhaps the Midrash is just using that terminology to explain just how corrupt and despicable the Dor HaMabul was. That, essentially (though perhaps not literally), they used every loophole they could think of to be within the law but outside the bounds of morality or simple human decency and therefore deserved to be punished and wiped out. Bnei Noaḥ then, perhaps, were given a stricter set of rules than they otherwise should have needed, either as punishment or as preventive measure against future corruption (or both). The Midrash does not have to be historically accurate with regard to how the courts generally worked in the days of the Dor HaMabul. On the other hand, it could even be that the Midrash has a Mesorah about one such case in which this happened, and it's pointing to that as a demonstration as to just how low they had gone to maintain the non-culpability with their behavior.
I'm not convinced that the courts at that time used Bnei Yisrael's system of Halachah with regard to determining the minimum amount of money for which a thief is liable, though I remain open to that possibility. I am, however, fairly certain that the Midrash is using the example of deliberate less-than-Perutah theft to show how evil they were (because you must agree that this is evil) OR to make a point (you may not think this is evil, but see what happens if you employ this type of tactic!).
The only viable answer seems to be that then, as now, there was no legal responsibility under Divine law for stealing less than a perutah's worth, despite sources that on their surface state otherwise.
Since under Noahide law, according to the Rambam, the punishment for violation of any of the 7 laws is the death penalty, it cannot be that such a harsh penalty applied to stealing less than a perutah's worth (less than a nickel today).
G-d does not promulgate laws that would constitute a chillul Hashem.