I've asked Can an embedded audio player be added to Audio.SE and Music.SE?, I've gave someone a bounty but that doesn't mean the feature request has been answered or handled. Yet, it is marked as have been answered in the list of questinos. Is this a bug?
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It's displayed as "answered" because it has one answer with at least one upvote. This has nothing to do with whether or not you've accepted an answer, nor is it because you've awarded a bounty.
By contrast, "unanswered" means that none of the answers to the question have been upvoted and that none of the answers have been accepted.
This entry in the FAQ provides support for the conclusion, although it doesn't directly address the question that you asked.
You mean that it isn't listed under "Unanswered"? This is because it has at least one answer, and at least one answer is upvoted. There are 2 answers, one at +2 score and one at +1 score, which makes it fail the criteria for "Unanswered". The bounty has nothing to do with it, although bounties typically lead to answers that ideally get upvoted.
Not being listed as "Unanswered" does not mean that we think the request has been handled. It'd need to have an Accepted Answer (which it does not, and it is one of the 4 questions currently docking your accept rate, just to assert that it is not possessing an accepted answer), or an appropriate tag such as status-completed. Lacking those, people generally assume that such a request is not handled, no matter how many bounties have been assigned. Such as this request, which has had several bounties - we all still know it's an open request.