I re-installed over the weekend. It doesn't do anything. The software works fine on an account with administrator privileges. It does not work with a standard user. Steam auto updates when it is opened, but it doesn't ask for administrator credentials. It just throws the error that it is damaged.
But, I just figured it out. I opened a Terminal and ran Steam as the superuser with the following command:
sudo /Applications/Steam.app/Contents/MacOS/steam.sh
It ran the update and then exited. When I double clicked on Steam in the Finder, it opened like it should.
I first had to go back into my administrator account and edit the /private/etc/sudoers file to add the kid's account. Otherwise, you can't use sudo. So, technically now the kids can get admin privileges on the command line, but they don't know unix. Security through obscurity :-)
If this is too complicated, then just run Steam in an account that has Administrator privileges and it should work. Hopefully they fix this in a future release. Origin doesn't have this problem...