Afaik Leonard never liked playing that game, so whenever Sheldon suggests it, he gives in to avoid any arguments.

Leonard: "Well, I want to watch it now."

Sheldon: "Then I believe we’ve arrived at another quintessential 'rock, paper, scissors, lizard, Spock' moment."

Leonard: "Watch whatever you want."

Raj (looking at Sheldon): "I saw what you did there."

Sheldon: "What did I do?"

Side note:

Sheldon should know not to always choose 'Spock'. As a kid he played 'rock, paper, scissors, candy, pony' with Missy and he always won, because she always chose 'pony', and he knew that.

• Young Sheldon: "Rock, paper, scissors, candy, pony"

@mechajutaro said:

Why didn't Leonard accept Sheldon's challenge over watching the Clone Wars movie?

My guess: He's seen RedLetterMedia/Plinkett's reviews of each of those stomach churning prequels, and knows better than to say "Yes" to Sheldon's offer

But he wanted to watch it before Sheldon said that he (Sheldon) didn't. If Leonard thought/knew it was bad, he should have not wanted to watch it to start with.

Apparently he wanted to watch it so little, that even a sure-win "Rock, Paper, Scissors, Lizard, Spock" wasn't worth it.