It occurred to me that an alternative to considering whether Stephen Crane's "The Blue Hotel" measures up to Tolstoy's standards of good art, you might write your essay on the subject of how bad art has apparently had a seriously harmful influence on the Swede and is directly responsible for his death as well as the imprisonment of the gambler who kills him. The bad art I am referring to is the so-called dime-novels which paint a lurid picture of the Wild West. These have given the Swede such an unrealistic impression that he fully expects to be murdered. There are numerous references throughout the story to the Swede's apparent fear of everyone, amounting to acute paranoia. But the Easterner spells it out clearly in the following excerpt.
"Why, he's frightened!" The Easterner knocked his pipe against a rim of the stove. "He's clear frightened out of his boots."
"What at?" cried Johnnie and the cowboy together.
The Easterner reflected over his answer.
"What at?" cried the others again.
"Oh, I don't know, but it seems to me this man has been reading dime-novels, and he thinks he's right out in the middle of it--the shootin' and stabbin' and all."
Tolstoy devotes many pages to what he calls "counterfeit art." The dime-novels about the Wild West were certainly good examples of that. Most of the hack writers who cranked out these lurid stories knew nothing about the real West. They made up anything that occurred to their imaginations and copied the atrocious fabrications of other hacks. Stephen Crane's "The Blue Hotel" is largely based on a contrast between the real West and the fictitious Wild West where there was no law, no civilization, and violence was the norm. Tolstoy would say that good art has a beneficial influence on society, whereas bad art has just the opposite effect.
Tolstoy describes the methods of producing counterfeit art in Chapter Eleven of his book. The four methods he identifies are borrowing, imitating, striking (creating effects), and interesting. All of these were to be found in the dime-novels about the Wild West, perhaps especially "creating effects." The Swede was probably more impressionable because he was a foreigner and a newcomer to America.
Tolstoy's conception of art as expressed in his essay "What is Art?" is somewhat difficult to apply in a practical fashion as a tool of literary criticism, as one of its criteria for evaluating a work is sincerity, something we cannot actually judge from the outside. Tolstoy suggests however that a second criterion is that the feelings must have adequate expression. Thus as you analyze Crane's story, you might focus on whether the Swede's behavior is credible, and whether the narration, positioning us to take a puzzled external view of the Swede, strengthens the ending or weakens the story.
A major thesis of Tolstoy's essay is that while art can be amoral, and judged on the grounds of some form of aesthetic pleasure, whether grounded in idealism or reader response, great art is that which contributes to the moral development of the human race. This is how art justifies its existence, and what makes spending money on art rather than on feeding the poor ethically justifiable.
In your conclusion, you should discuss whether the ending of the story, in which we find out that Johnnie was, in fact, cheating, and his friends colluding with him, creates the sort of moral impact Tolstoy admires.