That's odd. :S The integrity check is new, to avoid difficult to track down problems with antivirus and anti-malware mucking around with Spine files (though probably not an issue on Linux). It's possible we need to be a bit smarter about it.
I'm able to download, extract, and run Spine on Lubuntu. Is it possible something is modifying or adding a file to the jre folder? Maybe desktop environment metadata or something similar?
Sorry you are running into this trouble! We'd like to get this fixed ASAP, but first need to understand why the check is failing.
New launcher (3.7.30) is up, can you please check if it is working correctly now?