I was able to get it running again by finding the app in the root application folder and doing the following:
Right click Minecraft.app
Get info
Set permissions to Read & Write for all entries
Click OK
Show package contents
Right click the directory "Contents"
Click the lock icon and authenticate
Click the gear and select Apply to all enclosed items
Run program.
More work than moving to the ~username/Applications, but then you don't have to move the application from where it should actually be installed.
I was able to get it running again by finding the app in the root application folder and doing the following:
Right click Minecraft.app
Get info
Set permissions to Read & Write for all entries
Click OK
Right click Minecraft.app
Show package contents
Right click the directory "Contents"
Get info
Click the lock icon and authenticate
Set permissions to Read & Write for all entries
Click the gear and select Apply to all enclosed items
Click OK
Run program.
More work than moving to the ~username/Applications, but then you don't have to move the application from where it should actually be installed.