Let's look at the realism angle first. Victorian literature does not necessarily take a gritty and graphic approach to...
I believe that two main elements of Victorian literature can be found in this Mark Twain story. Those two elements are realism and a focus on class distinctions in society.
Let's look at the realism angle first. Victorian literature does not necessarily take a gritty and graphic approach to realism. Victorian realism is much more focused on daily life, reflecting common and practical problems potentially experienced by English subjects of the time. "The Million Pound Bank Note" incorporates this element through Henry's character. Henry is definitely a common man, struggling to make his intended fortune.
When I was twenty-seven years old, I was a mining-broker's clerk in San Francisco, and an expert in all the details of stock traffic. I was alone in the world, and had nothing to depend upon but my wits and a clean reputation; but these were setting my feet in the road to eventual fortune, and I was content with the prospect.
By the time he arrives in London, Henry has a single dollar to his name. It is not enough to buy food or clothing with, and his body begs for food scraps that have been thrown away.
I stopped, of course, and fastened my desiring eye on that muddy treasure. My mouth watered for it, my stomach craved it, my whole being begged for it.
Even after Henry is given the million pound bank note, the story still focuses on problems that are fairly mundane. He cannot buy anything with the bank note, because nobody can cash it and give him change.
It is useless to me, as useless as a handful of ashes, and yet I must take care of it, and watch over it, while I beg my living. I couldn't give it away, if I should try, for neither honest citizen nor highwayman would accept it or meddle with it for anything.
That problem is eventually sidestepped because everybody starts allowing him to buy on credit.
A second Victorian element of the story is its emphasis on the importance of class status. Henry is not content to be a clerk. He wants to be a wealthy gentleman. He's able to use his million pound bank note to work his way there. The bank note gives him the ability to buy everything on credit, and he quickly becomes famous. He is known as the "vest-pocket million-pounder." Newspapers write about him more than the nobles.
I was listed above the knights, next above the baronets, next above the barons, and so on, and so on, climbing steadily, as my notoriety augmented, until I reached the highest altitude possible, and there I remained, taking precedence of all dukes not royal.
It is at this point that Henry believes that he has finally made it. Fame and fortune is his definition of success. Henry eventually is able to use his influence to make an actual, real fortune; therefore, when the story wraps up, he does not need the payout of the bet. He's already become a gentleman and a member of the upper class. He has reached his initial and ultimate goal.
"But wait, wait! The situation, you know. I want to give you the situation," said my man.
"Well," I said, "I'm just as grateful as I can be, but really I don't want one."