Laura never appears in the story, but she's still super important. For starters, she's the only character in the story with a name. So…what's up with that?
Though "King of the Bingo Game" is in the third person, we're incredibly close to our protagonist's perspective. And what's the most important thing in the world to our protagonist? What is the one thing that receives his focus? Laura. Exactly. No one else in the bingo hall particularly matters. Ellison very subtly puts the story in the hands of his protagonist by allowing his character's mindset to determine certain narrative elements. (You can read more on this in "Narrator Point of View.")
You can view the protagonist's eventual failure regarding Laura in a couple different ways: do you think he really and truly let her down by failing to release the button and shoot for the jackpot? If he had stuck to the plan, after all, he could have had a decent shot at winning the jackpot.