According to our gemara, grama is mutar on Shabbos. Yet, I thought that in Baba Kama we learnt that only B'nizikin grama is patur but not on Shabbat?
You are referring to the Gemara on Daf 60a in Bava Kama, which says that one who winnows (Zoreh) on Shabbos is Chayav even though the wind assisted his act, because the Torah forbids any Meleches Mach'sheves, and he had intention to perform the Melachah that was accomplished. He is Chayav in such a case on Shabbos even though his act only caused (Grama) the wheat to be winnowed.
Nevertheless, it seems clear that the case in Bava Kama cannot be compared to our Sugya which says that causing (Grama) a fire to become extinguished on Shabbos is permissible. Even if Grama is Chayav on Shabbos, this applies only when one performed the act in the normal manner of doing the Melachah (such as throwing the wheat into the wind, in the case of winnowing). In our case, though, besides Grama, the person is using an unusual manner of extinguishing (k'l'Achar Yad), and therefore one is not Chayav for it on Shabbos.