The narrator of The Natural doesn't get his or her hands dirty. All of the narration is done with an emotional no-man's-land between the narrator and the action. For example, check out this passage: "The Knights took their three in Boston and the next day won a twi-night double header in Ebbets Field, making it seventeen straight wins on the comeback climb" (8.15). The narrator is far from the action, talking like a news reporter, which gives the novel a dry, distant tone.
Here's an example of what must have been one of the most emotional moments in Roy's life, getting his Knights team cap. He's finally realized his dream of playing in the majors.
"Try this for size." He handed him a blue cap with a white "K" stitched on the front of it.
[…] "How's it look?"
"A dream but why the tears?"
"I have a cold." He turned away. (2.72-79)
Not "Roy felt his eyes welling with tears as he said to himself, 'I've finally made it. All those years of hard work and I'm really here.' It was almost too much to bear and he struggled to hold back the tears." Nope. Just, "I have a cold."
This combo of distant, dry commentary with zoom-in close-ups gives the tone of The Natural its own special flavor. Emotionally, the reader is distanced from the tragedy because the tone is so matter-of-fact and distant. Even though we're watching someone we grow to care about (it's Roy; stay with us) experience personal tragedy, it's not a tearjerker like Old Yeller. The distance helps us to see it as a more epic, dramatic novel. The characters in it can seem like types rather than real people.
Having said that, Shmoop does think there's emotional tone in the novel. It's just that the tone is pretty depressive and hopeless, which adds to the feeling of distance and deadness. Depression is emotion, but it can feel like the absence of emotion.