PY: Thank you for bringing another 2 teshuvos from Reb Moshe, in addition to the one I quoted, where he clearly writes that one may not extinguish or even lower a gas flame on an oven even with a pilot light on YT unless it is clearly ochel nefesh such as preventing the food from burning. It is also obvious from these 3 teshuvos that Reb Moshe did NOT consider turning off the gas GRAM kibuyi, rather it is proper kibuyi. I did a little bit of research and found that the Machaze Avraham, Be’er Moshe, Tzitz Eliezer, Agudas Aizov, Yabia Omer, Shmiras Shabbos K’Hilchaso and R’ TP Frank all write that turning off the gas to a stove is considered True kibuyi and NOT Gramma. I think we can add to this list the Magen Avraham and Mishna Berura 514:15 who only permit removing a solid piece of tallow from a lamp on YT if it is distant from the fire and has not yet begun to melt and become connected to the fire. This condition would clearly exclude a gas oven. I’m still waiting to hear ANY source that considers it grama.
Kibuyi is not ALWAYS aina tzricha l’gufa, although it usually is. The Mishna in Ba’meh Madlikin quotes Reb Yossi who says that one is only chayav for extinguishing a fire if he needs the wick. The Gemorra Shabbos 31B brings a machlokes if Reb Yossi holds like Rebbi Yehuda or Rebbi Shimon regarding MSHETLG. The Rambam paskens like the first answer that he agrees with RY, but the majority opinion is that he agrees with RS and only considers kibuyi deoraisa when it is done with the expressed intention to create coals.