Whenever I read or write a question I tend to break it down into 3 parts:
What is the core question that is being asked? - Typically this will be the title of the question but not always.
What has the person tried to do so far to resolve it? - Typically the first few paragraphs of the question.
What difficulties have they ran into with that approach? - Typically the last few paragraphs.
So long as the core question that is being asked is on topic then the Question as a whole is on topic.
The caveat I would add to this is that there is no reading between the lines for the core question. If what an asker is trying to do is on topic but the question they have asked is off topic then I'd treat it as off topic.
I know some people on other Stacks who also judge a Question's topic-ness by the Answers it receives, I think this is unfair and that a question should be judged on its own merits with perhaps guidance given to the OP on how to adjust the question to better attract the answers expected if it is getting lots of off topic ones.
In the example you gave
So, applying this logic to the example you gave:
- The Core Question: How do I connect my computer to my GameCube?
- The attempt so far: "I've spliced into the cable as described here in order to use NintendoSpy..."
- The difficulties: "However, most people do this by using Arduinos and I am not willing to spend any money on this project..."
So for me this question is on topic because connecting to old gaming hardware is on topic. The fact he has went on to explain an approach that requires re-writing code is irrelevant, it's just the explanation of what he has tried so far and what issues he is having, an answer to the question doesn't need to take that into account at all to be valid. However, had the core question been "How do I re-write this Arduino code to work on the Redboard?" (which could be a foreseeable follow up question) then that would be off-topic.
Your answer to the example
I think your answer is a great example of an on topic question having an off topic answer.
You explain to him the trouble with his approach and you offer 2 solutions to his core problem: replace the code or replace the board. An explanation of how to do these would be off topic so you point him in the direction of where they would be on topic. Perfect. Had you started explaining how to re-code it then you'd be verging into off topic territory - but I wouldn't hold your off topicness against the OP.