In the UK its technically illegal to rip a CD to your own PC to back it up, for example, see the recent high court case(s) about it where the government won against Brennan (who make hifi gear which can do this) - no different to this app.
In 2014 the government passed a law making ripping explicitly legal. In 2015 the music industry sued and the High Court ruled that the law was contrary to some EU directive and thus invalid. But I don't know if that law was annulled by the court decision, or if it was merely dormant until we left the EU. The Brennan ripping devices are still on sale. Do you have a link to this case?
Part of the reason google/youtube are quasi-monopolistic is that they've already been through all of this, they've had the arguments and the lawsuits in various different territories, and they've reached agreements and paid money to deal with the copyright issues.
From a quick read of that, it appears that Mp3tunes lost the case, had a huge damages award made against them, as happens a lot, and the overall damages were deemed excessive and reduced to $750k.
I haven't actually read the case, but from the summaries I've seen it sounds like MP3Tunes won on the parts that matter when it comes to whether or not one can legally run a music locker service without permission from the copyright owners.
In particular is said that the DMCA safe harbor is available to such services, and that deduplication is not a problem.
MP3Tunes did not adequately deal with DMCA takedown requests so didn't get full safe harbor protection leaving them liable for some user's uploads. Also MP3Tunes' founder had infringing songs stored and they got nailed for those.
