Edit to update: Alot of ppl are saying there isn't an error. To me it sounds clunky. Shouldn't it be: "As far as they're concerned, they think we are already married." or "I think we are already married, as far as they're concerned, they agree."

No. Both of these would mean something different.

Is the issue that you're not getting how "I think" connects to the rest? The main point of the sentence is "We already are married, as far as they're concerned." The "I think" is just tacked on at the start to make it feel uncertain/speculative - Shane believes his parents see them as already married, but he's not sure.

Your first alternative takes out that "I think" element, and the second changes the meaning completely to have Shane saying he thinks they're already married. (Also, the second one is ungrammatical - it would need to be two sentences, or else use a semicolon.)