Are you supposed to say, "I'm going to the cinema tonight" or "I'm going to go to the cinema tonight"? The former is in the present continuous: is it wrong to use it to mean the future?
"I can't come tonight. I'm meeting James"
"I can't come tonight. I'm going to meet James"?
We use the present continuous when we have made arrangements for the future, as in your example with meeting James, and going to for our intentions. However, with 'going to go', we often drop the 'to go' because it sounds repetitious, so we use it for arrangements and intentions. It's correct to say 'I'm going to go to the cinema', but the other sounds more natural to me, whether I have bought the tickets or merely want to go.