כל הבאבד נפש אחת מישראל - מעלה עליו הכתוב כאילו איבד עולם מלא, רכל המקיים נפש אחת מישראל - מעלה הכתוב כאילו קיים עולם מלא
Whoever destroys a soul from Israel, the Scripture considers it as if he destroyed an entire world. And whoever saves a life from Israel, the Scripture considers it as if he saved an entire world.
The Gemara's reasoning there is based on the fact that Adam was created as a single human and yet propagated the entire human race; similarly, any human alive today could potentially be the ancestor of all of humanity for the future, and to destroy or save his life is likewise to destroy or save all of humanity. But if so, why should it matter whether the subject saved is a Jew? I say, is this not a non-sequitor?
The Jerusalem Talmud, Sanhedrin 4:1 (22a) omits מישראל "from Israel", reading only נפת אחת "a soul". And according to Rabbi Gil Student, here, the same reading is found in Pirkei deRabbi Eliezer ch. 47, Tanna debe Eliyahu Rabbah 11, and Yalkut Shimoni on Exodus 166.
According to Amitai Halevi (cf. here), Rambam in Hilkhot Sanhedrin 12:3 follows the Yerushalmi's reading. To quote Mechon Mamre's text (there it is 12:7):
לפיכך נברא אדם יחידי בעולם--ללמד שכל המאבד נפש אחת, מעלין עליו כאילו איבד עולם מלא, וכל המקיים נפש אחת, מעלין עליו כאילו קיים עולם מלא.
Therefore man was created individual and unique in the world: to teach that anyone who destroys a single soul, it is considered as if he has destroyed an entire world, and anyone who saves a single soul, it is considered as if he has saved an entire world.
Halevi there also says
Hameiri too bases his commentary on the Yerushalmi version, illustrating "the destruction of a whole world" by pointing out that Cain's murder of Abel eliminated all of his victm's descendents at one fell swoop. Abel, like Adam was not Jewish; he was not even the ancestor of Jews.
And note what Professor Menachem Kellner says (Farteitcht un Farbessert (On “Correcting” Maimonides)), note 16:
Mishnah Sanhedrin 4:5 [...] states “accordingly, only one man was created, to teach that one who destroys a single [Jewish] person is regarded by Scripture as if he had destroyed the entire world and one who saves a single [Jewish] person is regarded by Scripture as if he had saved the entire world.” As Ephraim Elimelekh Urbach has shown, the word mi-yisra’el (“Jewish”) is a relatively late insertion into the text of the mishnah. See E. E. Urbach, Mei-olamam shel hakhamim: Qovez mehqarim [World of the Sages] (Jerusalem: Magnes Press, 1988), pp. 561-577. Through a series of coincidences, I discovered what is apparently the earliest textual witness to the correct text: Koran 5, 27-32! See my note on the subject, Tarbiz, 75 (2006): 565-566.
I decided to check the Koran's reading. The context of Koran 5:27-32 is Cain's killing Abel (very much like Meiri!); according to the Holy E-Books English translation of 5:32:
On that account: We ordained for the Children of Israel that if any one slew a person - unless it be for murder or for spreading mischief in the land - it would be as if he slew the whole people: and if any one saved a life, it would be as if he saved the life of the whole people. Then although there came to them Our apostles with clear signs, yet, even after that, many of them continued to commit excesses in the land.(R' Micha Berger, here, points out that the Koran speaks of "as if he slew the whole people", with "the" apparently referring to the Jewish people, like the particularist version of Sanhedrin 4:5. However, it seems to me that given that the Koran is basing itself on Cain's killing Abel, presumably it, like Meiri, universalistically views the victim's Jewishness as inconsequential, since Abel was neither Jewish nor the progenator of Jews. R' Simon Montagu confirmed my guess from the original Arabic: he says alnas `aljamia should be translated as "all of humanity", and adds that this whole passage has been variously translated as "he who saveth a life shall be as though he had saved all mankind alive" (J. M. Rodwell, 1909) and "hamehhaye [nefesh] ke'ilu hehhya et kol ha'adam yahhdav" (Hebrew for "one who saves a life is as if he saved all of humanity collectively", Y. Y. Rivlin 1987).)