His cigar was knocked out of his hand by the sail when it was blown in the wind and then he was knocked overboard
Well recalled! It was a pipe knocked out of his mouth by a rope, not a cigar knocked out of his hand by a sail, but that’s close enough:
Rainsford sprang up and moved quickly to the rail, mystified. He strained his eyes in the direction from which the reports had come, but it was like trying to see through a blanket. He leaped upon the rail and balanced himself there, to get greater elevation; his pipe, striking a rope, was knocked from his mouth. He lunged for it; a short, hoarse cry came from his lips as he realized he had reached too far and had lost his balance. The cry was pinched off short as the blood-warm waters of the Caribbean Sea closed over his head.
As for the meat of the question, well, different people use the word ‘literature’ in different ways. There’s a spectrum of opinions on the meaning of the word, which I’ll caricature like this:
- extreme inclusionist: “literature is anything consisting of words”
- moderate inclusionist: “literature is language deliberately put into permanent form”
- most people: “literature is poetry, plays, stories, essays, stuff like that”
- moderate exclusionist: “literature is written works of high quality, as judged by me”
- extreme exclusionist: “literature is the Bible and Shakespeare and Milton; all else is dross”
So when someone’s asked, “Is ‘The Most Dangerous Game’ literature?”, the answer depends on where they stand on the meaning of ‘literature’. People in groups 1–3 will answer ‘yes’ and maybe even some people in group 4, depending on what criteria they use to judge quality.
We can guess from your account that your teacher was a moderate exclusionist, and that an important criterion which she used to judge quality was literary realism, that is, the depiction of the subject in a realistic and naturalistic way. See this answer for more about literary realism and how it rejected the use of coincidence.
Literary realism had its heyday in the late 19th and early 20th centuries, and I think that you’d have to search fairly hard these days to find someone taking a position as exclusionary as your teacher’s.