Finally I found a solution.
Play Music works again after disabling experimental QUIC protocol here: chrome://flags/?search=quic#enable-quic

Addition (can't find how to edit post): this url works well in private window.

I have the same issue and can confirm that link from @greenriverrus returns 404 in opera 41+ but downloads ok even with curl.
I'm tried to make curl link in developer console:

curl 'https://r6---sn-gxuog0-bvwe.c.doc-0-0-sj.sj.googleusercontent.com/crossdomain.xml' -H 'Referer: https://play.google.com/music/listen' -H 'User-Agent: Mozilla/5.0 (X11; Linux x86_64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/55.0.2883.35 Safari/537.36 OPR/42.0.2393.38 (Edition beta)' -H 'X-Requested-With: ShockwaveFlash/23.0.0.205' --compressed

and it works well, page exists:

<?xml version="1.0"?>
<!DOCTYPE cross-domain-policy SYSTEM "http://www.macromedia.com/xml/dtds/cross-domain-policy.dtd">
<cross-domain-policy>
<allow-access-from domain="s.ytimg.com" />
<allow-access-from domain="*.youtube.com" />
<allow-access-from domain="play-music.gstatic.com" />
</cross-domain-policy>

Last working version of opera-beta: 40.0.2308.52.