Disclaimer, I've never used this module. Looking at the test in question the first thing that jumps out to me is this:

my $ua = Net::Amazon->new(
    token         => 'YOUR_AMZN_TOKEN',
    secret_key  => 'YOUR_AMZN_SECRET_KEY',
    # response_dump => 1,
);
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Suggesting you'd need to provide a valid token/key from Amazon. Then if you look at the error it tells you that Net::Amazon expects something that is not passed to it, the associate tag. The Changes file states:

0.61 (10/28/2011)
(cb) rt 71937; Amazon now requires an Associate Tag, so enforce usage.
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Music::Tag::Amazon has not been updated since 2010, and won't work because it's dependency (Net::Amazon) has changed to meet the requirement of the Amazon service. Fixing this would seem fairly trivial, and you can raise an issue and provide a patch via cpan.

Update: I don't have an Amazon soap account/developer tokens. I've made a very quick update, it's not final as I'd like to improve the tests and documentation more before raising the pull request. Please test this and let me know if it works.