The return value isn't automatically stored anywhere. You need to store it manually:
result = results(player1, player2)
if result == 1:
...
If you look up at the top of your code, you'll see you already did the right thing with the input
function:
player1 = input ("Player 1: Please enter either Rock, Paper or Scissors:")
Functions you define yourself should be handled the same way.
In response to the edit: Creating a local variable inside results
won't help. The code that calls the function needs to store the return value. (People have designed languages that work the way you're trying to get it to work. The result is a huge headache with unrelated parts of the program stomping over each other's data.)