An interesting perspective is this blog article by the developers of Prismata, a multiplayer card game. It doesn't directly answer your question of how you can make Rock Paper Scissor in a video game be more luck based but it's good reading in my opinion.
To directly answer the original question, here's a variation of Rock Paper Scissors that I tried to come up with. Instead of one round, let the players play multiple rounds of Rock Paper Scissors and decide the winner based on who won the most number of points in the end. Now add an additional action that players can do each turn: up the point value of one of Rock, Paper, or Scissors. To make the game more interesting, the other player cannot see what point values your Rock, Paper, and Scissors skills are. Finally, when you win a round, the number of points you get is equal to the point value of what you threw.
I just made up this example and haven't playtested it to see if it adds interesting depth and an element of skill, but the general principles I used were:
1) Continuity and a sense of progression. This is achieved by playing multiple rounds and allowing your point values to accumulate.
2) Imperfect information. Each player has access to information that the other player doesn't.
3) Larger option space. Rock Paper Scissors is a bit limited in that you only have 3 options per round. I added another set of 3 options for increasing point values so there's 3x3 = 9 set of options per turn