The assumption behind this question is that every letter, every word and every verse of the Torah is measured out carefully. Thus, we see that from an extra vav, a halacha may be derived. When, in the discussions often found in the gemara, one Tanna interprets an extra word in one way to prove his point, we must take pains to explain how his disputant, the other Tanna, makes use of that extra word. When an entire narrative is repeated, as with Eliezer and Rivka, this is deemed extraordinary and goes to show Hashem's great esteem for the Avot. When in parashat Noach, the Torah adds a few words in one instance so as not to use the cruder language, this is deemed extraordinary against the usual background of brevity and so teaches us the importance of refined language.
To sum up, there is this well-established notion that the every jot and tittle of the Torah is deliberate and that there is no unneeded repetition. While on a peshat level, many Rishonim would talk about natural linguistic motivations for extra words -- e.g. kefel inyan bemilim shonot, at the very least, in the realm of midrash halacha and midrash aggadah, there should be no repetition to no deliberate purpose.
There should therefore exist a systematic interpretation of every seemingly extra letter, word, and phrase in the Torah.
Many years back, I read a scholarly book (though cannot remember the name) about midrash halacha. The author asserted that, though Chazal attempted to make such a systematic interpretation across Torah, they did NOT succeed in this. That is, if you look through all of midrash halacha (of a work of midrash halacha) to see that every pasuk is accounted for, and every extra word, according to each opinion, you will find gaps that are really gaps.
Your question is then about one of these apparent gaps.
I don't know if Chazal interpreted the extra split into pesukim here. I believe that they do.
See Sifra on these pesukim, and particularly this quote:
"את הגמל כי מעלה גרה הוא.. ואת השפן כי מעלה גרה הוא.. ואת הארנבת כי מעלה גרה היא" מה תלמוד לומר? אם לתיקון המקרא הרי כבר נאמר 'הגמל והארנבת והשפן כי מעלה גרה המה', ולמה באו? לרבות את הריבויים שאמרנו.
That is, it seems to ask why state separately these three, in three separate statements. And if for the purpose of Tikkun HaMikra (unclear what it is -- HaLivni says it is ambiguous and is the only place found in Rabbinic literature), it is already stated (Devarim 14:7) הגמל והארנבת והשפן כי מעלה גרה המה. Rather, it is to include all the ribuyim we have stated.
So one should then learn through this Sifra carefully to deduce which ribuyim are accomplished specifically by splitting it up in this manner.
Edit: Also, I saw the following in a parsha sheet this Shabbos - which is what called me back to answer this question in the first place: