I would agree that Ossana/McMurtry bring elements of the Romantic to their screenplay.
However, "Brokeback Mountain" and indeed Annie Proulx's opus is an exemplar of a syncretic naturalism. To perceive this, one has to revert to the text of the short story itself to see the features of naturalism, which was a late 19th century lashback to Victorian and Edwardian romanticism.
The features of naturalism in English/American literature, for example, show nature as hostile and forbidding, a force that cannot be easily overcome and whose whim dominates human existence and limits, even crushes it. One of the greatest American exemplars of naturalism are by immigrant novelists such as Ole Rolvaag, who wrote the seminal "Giants in the Earth" about his own grandparents' emigration from Norway to South Dakota. The hallmark of Annie Proulx's prose when she writes of the natural world in Wyoming is starkly unsentimental, animating nature with chilling clarity:
The first snow came early, on August 13th, piling up a foot, but was followed by a quick melt. The next week Joe Aguirre sent word to bring them down, another, bigger storm was moving in from the Pacific, and they packed in the game and moved off the mountain with the sheep, stones rolling at their heels, purple cloud crowding in from the west and the metal smell of coming snow pressing them on. The mountain boiled with demonic energy, glazed with flickering broken-cloud light; the wind combed the grass and drew from the damaged krummholz and slit rock a bestial drone. As they descended the slope Ennis felt he was in a slow-motion, but headlong, irreversible fall.
The very stones chased them down the mountain, hastened by the wind. There is no friendly Nature here, no triumph of human spirit. The "demonic energy" of the mountain gives it a life far more than that of a volcano or other natural event - but that of THE most hostile spirit: and the wind, animating the the weather-stunted trees (krummholz - stunted trees) and the inanimate rock with "a bestial drone." This is stark naturalistic style, and it is very, very similar to Rolvaag and even to Steinbeck's naturalism.
In the Naturalistic prose tradition, nature plays a hostile and limiting role, and Annie uses this to illuminate that just as Nature is hostile to man, so Society is hostile to the passion Jack and Ennis found, so they were doubly bound, and doubly condemned.