In The Perfect Storm the antagonist was a rival fisherman who helps to drive the MC (on top of financial stress) via professional competition to take an extreme action in the face of danger.

‘Cast Away’ and ‘All Is Lost’ are exceptions in the genre. Naming examples is a risky thing to do because for every example supporting one argument you can find one if not more supporting another.
To that matter here is a little list, off the top of my head, of successful Man V nature films that had an antagonist separate to the force of nature: Twister, Volcano, Titanic (yes the story with in the story is man V nature many men and women V nature in fact but since the story was weak on its own they strung a romance story with an antagonist into it which is likely what made it so successful), The Mountain, The Grey, Dante’s Peak (Paul who doesn’t believe Harry, not a long plaid role but enough to create a dramatic premise), The Poseidon Adventure (actually has several antagonists spread across all acts) the list goes on…

Point is while a few films in the genre worked well with no antagonist the fact is that the majority of successful films in this genre did have antagonists. This is a point worth noting and implementing when writing in the genre.