This is pretty much how I felt about it too:
Nothing Happens in GWENDY’S BUTTON BOX – Dark Moon Digest
It's not a bad read, but it feels like it was about so little in the end.
I think the hat comes from the character of Mr. Steward (from the story this was obviously based on, 'Button, Button' by Richard Matheson) who is said to wear a hat. Actually it was filmed twice, both for the Twilight Zone '80s run, and later as a feature film, The Box with Cameron Diaz by Richard 'Donnie Darko' Kelly.
To Matheson's dismay they changed the ending for the Twilight Zone episode which he had adapted himself, so he used his standard pseudonym of Logan Swanson for that. Actually I kind of like both the original and the alternative Twilight Zone ending.
The main difference between the two stories, is that the Matheson story is all about 'would you push the button if you didn't know the person who got killed and you got a large sum of money for it'. Gwendy already gets rewarded by the chocolates and coins, so it's only curiosity that tempts her to use the buttons, which makes the idea weaker overall.
And as for the R.F. initials: there was nothing really evil about the Richard Farris character, so I'd say that's a coincidence.