Additionally after booting once again I found these in the log:
18.02.12 21:39:59,270 com.apple.kextcache: Can't open CFBundle for /System/Library/Extensions/prl_hid_hook.kext.
18.02.12 21:39:59,270 com.apple.kextcache: Can't open CFBundle for /System/Library/Extensions/prl_hypervisor.kext.
18.02.12 21:39:59,271 com.apple.kextcache: Can't open CFBundle for /System/Library/Extensions/prl_netbridge.kext.
18.02.12 21:39:59,271 com.apple.kextcache: Can't open CFBundle for /System/Library/Extensions/prl_usb_connect.kext.
18.02.12 21:39:59,271 com.apple.kextcache: Can't open CFBundle for /System/Library/Extensions/prl_vnic.kext.
18.02.12 21:39:59,359 com.apple.kextcache: Can't open CFBundle for /System/Library/Extensions/prl_hid_hook.kext.
18.02.12 21:39:59,360 com.apple.kextcache: Can't open CFBundle for /System/Library/Extensions/prl_hypervisor.kext.
18.02.12 21:39:59,360 com.apple.kextcache: Can't open CFBundle for /System/Library/Extensions/prl_netbridge.kext.
18.02.12 21:39:59,360 com.apple.kextcache: Can't open CFBundle for /System/Library/Extensions/prl_usb_connect.kext.
18.02.12 21:39:59,360 com.apple.kextcache: Can't open CFBundle for /System/Library/Extensions/prl_vnic.kext.
Any help on that?
You can set the permissions back to root:wheel by running these:
sudo chown -R 0:0 "/Library/Parallels/Parallels Service.app/Contents/Kexts/10.6"
sudo chmod -R 755 "/Library/Parallels/Parallels Service.app/Contents/Kexts/10.6"
Then try the launcher once more.
OR
Try just reinstalling Parallels in ML. It will almost surely fix the issue and be far quicker than trying to troubleshoot.