What job is the noun clause doing in this sentence? whether we win or lose is not as important as having fun while trying?

The correct answer is the subject.

The subject of a sentence is a word, phrase, or an entire clause that is showing us who is performing a particular action. In the case above, the noun clause Whether we win or lose acts as the subject of the sentence. You can replace the entire sentence with a single word; for example, the pronoun SHE: She is not important... Therefore, it will be easier for you to determine that it is actually the subject.

fearlessness is your answer