I realize that this still may not answer the question:
Note that this identification is found in the Talmud Yerushalmi (Shevi'it 16a, also in Kiddushin, see below), as well as the Bavli (Bava Basra 56a), albeit in a different order, although all of these girsaos are questioned by mefarshim to make them uniform.
At this Otzar forum, we find a listing of places that Onkelos identifies geographical locations and nations by names that were familiar to those in his day, this being one of them (meaning that Salmai were the people in his day that were to be identified with this). This is first suggested by Ramban to Bereishis 41:45. According to this, he simply didn't know the current identification of the other nations.
The problem with that answer is that it should not carry over to the other Targumin that translate it similarly (especially since they sometimes repeat the Torah's name for a nation or place), such as Targum Yonasan above, and Targum Yerushalmi to Bamidbar 24:21 (one of the many other places that this translation appears), and nor did it necessarily retain the same name in the times of the Amoraim.
However, we can simply answer that since this was such an early connection (Onkelos and Chazal understood it this way), all these sources agreed with this correlation, and that's why it is so widespread among the translations. Also, in Lunz's Hameamer page 273, he identifies it with a city south of Beis She'an called Salumia in Arabic, which he claims is referred to in Yerushalmi Bava Basra 9b as שלומי.
This may also be the opinion of the Korban Haedah, as when the Yerushalmi Kiddushin 1:9 makes this same association, he says that there is no midrashic connection to these places, it was simply a known geographical location:
ה"ג רי"א שלמאה ערביי' נבטייה . הן ג' מדינות וגמרא גמיר ליה שהן ארץ קיני וקניזי וקדמוני:
If so, perhaps Onkelos was not familiar with the others.
Alternatively, Sefer Meir Ayin on Shoftim (page 4, here) notes 1 Divrei Hayamim 2:54-55 (below quote), which connects "Salma" to the house of "Keinim", suggesting that this was the name by which they were called later on, and thus referred to by an ancestor's name in the Targum, whereas we don't know the ancestors of the other nations:
בְּנֵ֣י שַׂלְמָ֗א בֵּ֥ית לֶ֙חֶם֙ וּנְט֣וֹפָתִ֔י עַטְר֖וֹת בֵּ֣ית יוֹאָ֑ב וַחֲצִ֥י הַמָּנַחְתִּ֖י הַצׇּרְעִֽי׃
וּמִשְׁפְּח֤וֹת סֹֽפְרִים֙ [יֹשְׁבֵ֣י] (ישבו) יַעְבֵּ֔ץ תִּרְעָתִ֥ים שִׁמְעָתִ֖ים שׂוּכָתִ֑ים הֵ֚מָּה הַקִּינִ֣ים הַבָּאִ֔ים מֵחַמַּ֖ת אֲבִ֥י בֵית־רֵכָֽב׃
In his JSTOR article, Dov Rappel notes that no one is really sure of the answer to this question, but also notes the Midrashic association that we did above. He also suggests that it שלמאי may be an Aramaic translation of the word קיני, but doesn't explain why Onkelos and others would translate the name of this nation specifically.
None of the classic Mefarshei Onkelos here (such as those listed on this page) provide any serious insight. Nesinah Lager (R' Nosson Adler) references Shir's article in Bikkurei Haittim 5584 (link at the bottom of that page), which my computer is loading really slowly, so I can't look it up. He also notes Ibn Ezra, which likely refers to the fact that these nations have two names, and perhaps he understood that to mean that Salmai was their real name.
I might suggest (kind of the opposite of Sefer Meir Ayin) that the Keni may have been named after a person named Kayin, but that was not how the nation was known in the times of Chazal/Onkelos, whereas the names of the others were pure names of nations, and not named after an individual.
For further reading about the Keini, see mefarshim to this Passuk (Bereishis 15:19), particularly Radak.
