Concerned I may have accidentally dropped malware (or something) onto my system
It looks like you did your due diligence and there is no evidence of a real malware problem - it sounds like their installer just screwed up the permissions.
Fire up Terminal, and do an ls -l of your Applications folder, looking for the QMC2 folder. I'd be willing to be it did something like installing as root (I bet the package asked for your password, right?) and missed correcting the permissions.
Once you've found it, you can do a chown (your username) -R (QMC2 path) to set everything to your user.