First I'd apologize for I can't describe it clearly. I've heard that "scissors cut paper" is correct, but I found Sheldon said "scissors cuts paper" in The Big Bang Theory. Which is correct, or both of them?
In this case you are talking about the option you choose in a game. You could read the sentence as
The option scissors cuts the option paper
Scissors cuts paper
So while "scissors" is plural and you would always say "scissors cut paper", in this case the word refers to an option within the game (singular) rather then the actual item.
Compare with "scissors are better than ..... " if you are a fan of sharp metal things, but if you are talking about the game you'd get "(the choice of) scissors IS better than ..."
The reference is to the US tv show 'The Big Bang Theory', and to one of its main characters Dr Sheldon Cooper. He speaks excellent if highly idiosyncratic English. I listened carefully to a video and he does say 'cuts'. While grammatically 'scissors cut paper' is correct, explanations on the internet of the standard game 'rock-paper-scissors' and the Big Bang Theory game 'rock-paper-scissors-lizard-Spock' (which Sheldon attributes to 'the internet pioneer Sam Kass') vary between 'scissors cut paper' and 'scissors cuts paper'. Possibly the use of 'cuts' is influenced by the fact that all the other choices in the game are singular, and therefore use 'cuts' eg 'paper covers rock'.
A few words, though singular in nature, are made of paired items and generally treated as plural:
scissors, pants, trousers, glasses, pliers, tongs, tweezers, and the like. Many are often used with the word pair as in pair of pants or pair of scissors. (Tricky Plurals)
So the correct version in your case would be "scissors cut paper".
I think, the reason for confusion is:
scissors cut paper,
a pair of scissors cuts paper.
I agree with Esoteric. In the game "scissors" is a choice in the game - a title, if you will.
So, you might say "the choice of scissors" cuts the choice of paper.
"Choice" is singular, so you use "cuts"
Maybe more clear if you enclose scissors in quotes, as such: "Scissors" cuts "paper."
If you are talking about the tool made up of 2 scissors, you would say "scissors cut paper" because "scissors" is plural. I know this because I never say "This scissors is sharp." I always say "These scissors are sharp." So the tool is made up of two things, two scissors, and they cut. They don't cuts.
I have seen the same question come up with bands such as "The Ramones" and "The Replacements" and "The Bare Naked Ladies"
The Ramones rock ! Or "The Ramones" rocks !
Depends on if you are talking about a singular band called "The Ramones" or multiple Ramones.
Multiple Ramones definitely rock. But the band called "The Ramones" rocks. So The Ramones rock. But "The Ramones" rocks.
There is no doubt, however about The Cure, which is a singular name. With or without quotes, The Cure sucks.
I think the correct point in this is that scissors do cut paper. But when describing the action happening now a way of saying scissors are cutting the paper is 'scissors cuts paper'.
When you play the game and scissor and paper comes up then then the scissors cuts (the) paper.