It's a difficult undertaking, maestrowork. I believe few writers can pull it off and keep the story interesting. It usually involves a solitary character, with mostly him and his surroundings presented to the reader. The story will lack important pacing elements, which the missing dialogue won't help to move along, and there's little conflict between characters to build tension.
When it's been done, and done well, there's plenty of internal conflict the MC must deal with, and that helps with the story's appeal. The reader will become intimate with the character early on, for there isn't much else for the reader to hold on to. The key is to make the MC so interesting, so entertaining and fallible, that the reader can't help but continue onward to the story's conclusion.
Hemingway does it so well that you never realize anything’s missing, in particular, spoken words. You become engrossed in the MC’s plight to such an extent that nothing else matters except how things will end for him.
That story has lived inside me for thirty years, through multiple readings. It doesn't get any smaller or larger, but it stays there just the same. It may never leave me until I'm gone, and even then, I'd like to take it with me.