I hadn't even heard of this story until I encountered it in e-Notes. I found it interesting. That is, it held my attention to the end. But I can't say that I found it "entertaining." It seems old-fashioned even to me, though I am old enough to be a grandfather. I would guess that it would seem terribly old-fashioned to young readers who are much more sophisticated about humor and comedy because they have seen so much of it in movies and on television. The story comes close to being a dirty joke. There are many dirty jokes that are based on the bad smell of something other than Limburger cheese. That is called scatological humor, and "The Invalid's Story" might be called scatological. Also, the idea of making a funny story out of decaying corpse seems not to be in the best of taste. But this story was written a long time ago, and Americans were much simpler in Mark Twain's time. Most Americans lived on farms or in small towns.
I found the story interesting because it shows how a talented writer can evoke a sense of smell in a reader's imagination and also how an entire story can be based on single effect such as a bad smell. I don't think "An Invalid's Story" is typical of Mark Twain's best writing. It strikes me as being something he wrote for his own amusement when he had nothing better in mind to write about. It shows his power as a writer. He was a genius. He could take anything at all and make it into a story or an essay. This is more or less what he did with a bullfrog in his well-known story "The Celebrated Jumping Frog of Calaveras County." A hundred and fifty years later they are still holding an annual jumping frog contest in Calaveras County in Northern California in commemoration of Mark Twain's story.