It is apparent from 15:16 which you quote that Emorite is the nation chosen to represent all the nations of Caanan. In fact in the artscroll English chumash it says as much.
The Medrash Rabba that Rashi 48:22 is quoting goes further and darshans that which I took from the hands of the Emorite as meaning from Chamor the father of Shechem. The medrash asks but was he an Amorite? And answers the Chivi are included in the Emori.
Same idea as mentioned above.
But getting back to 15:16 we are left to wonder why choose the Emori to represent all of Canaan. There are a number of explanations brought in Shaarei Aharon on that verse, some which may answer your original question by themselves.
- Ramban Rabeinu Bachia and Radak say they were the strongest nation as seen in Amos 3.
- Maskil LiDovid says their allotment of sinning was filed first as we find Sichon king of the Emorim getting conquered first. Numbers 21.
- The Netziv says the opposite and the iniquity of the Emori was the last to be filled, but being that they were the main inhabitants of the land at the time the Bnei Yisroel entered the land, the timing was based around them.
- Ba'er Basadeh says the Emorite had the most zchusim being that Enor Eshkol and Mamrei, the people involved with Avraham's bris were all in the field of Mamrei the Emori.