For a short novel to be a novella, it has to be somewhere between 50 and 100 pages long when published in a regular sized book. And there would be 30 to 40 lines of text on a page.
But, even the little 4 3/4" x 7 1/4" (12 cm. x 18 cm.) sized stand-alone paperback edition of Brokeback Mountain only has 23 lines per page and lines-wise, only 52 pages of text.
So, Brokeback Mountain is not a novella, IMO; it is a short story.