Who is the narrator, can she or he read minds, and, more importantly, can we trust her or him?
Third Person Omniscient
We've got a third person narrator here, and he's pretty omniscient. He even starts with a look at the scenery, saying "A few miles south of the Soledad, the Salinas River drops in close to the hillside bank and runs deep and green" (1). Oh, and he also knows what's going on with all the characters at all times.
One interesting thing, though: our narrator doesn't do much traveling into characters' minds. He tells us occasionally that a character "frowned as he thought" (2) or "thought for a moment," but he never actually tells us what the character thinks.
Instead, all our insight into these characters comes from description. George lays his cards down "thoughtfully" (2); Lennie's eyes are "frightened" (2); Curley's wife speaks "playfully" (2). It's almost as though Steinbeck is deliberately withholding insider information—maybe as a mirror to the characters in the play.
In this hard-hitting, straight-shooting story, it simply wouldn't be fitting to have a narrator gushing about how everyone feels all the time. Without personal commentary or much narrative insight, actions and speech do the work of exposing characters.