Ernest Hemingway always writes with a simple and almost journalistic style. In "A Clean, Well-Lighted Place," he is perhaps even more minimalistic than ever. 

Your question refers to vocabulary, so it is essential look at some sample sentences to determine whether the language is simple or erudite (learned and scholarly). These three representative sentences come from the beginning, middle, and end of the story.

In the day time the street was dusty, but at night the dew settled the dust and the old man liked to sit late because he was deaf and now at night it was quiet and he felt the difference.

Notice the use of the simple terms: dusty, dew, old man, deaf, and quiet. All of these words are part of a basic vocabulary which even a child could understand. On the other hand, there are no vocabulary words which could be considered scholarly.

The same is true of this sentence:

The waiter poured on into the glass so that the brandy slopped over and ran down the stem into the top saucer of the pile.

The waiter pours (not decants or dispenses) into a glass (not a goblet or a tumbler), and the beverage slops and runs (not courses and streams) into the saucer which is in a pile (not a mound or a quantity).

The last sentence is consistent with the others.

Turning off the electric light he continued the conversation with himself

The vocabulary in this story is as simple and basic as the old men  (one of whom is a waiter)about whom the story is told. The vocabulary is perfectly suited to the simplicity of a story about shared loneliness and despair.