I have solved the issue, thanks to a completely unrelated problem that had the same solution. My OS is the N version of Win10, which means it is missing many features associated with Windows Media Player. I believe one of those features is necessary to play these files through Opera, though I don't know which. As soon as I downloaded the feature pack here
(you may have to search for the pack dedicated to your version of windows)
the problem stopped.
Please let us all know if the same fix works for you.