Any admin on a site receives Contact Us emails. However, in order to have a better workflow and to know who is doing what, it would be better if institution admins received only Contact Us messages that were sent by members of their institution instead of any message. Many messages may pertain to things that they don't know about and thus should not receive messages as then nobody feels responsible for them.
Thus:
Contact Us message from logged out user -> Site Admin
Contact Us message from logged in user No institution -> Site Admin
Contact Us message from logged in user with institution -> Institution admin / admins if in multiple institutions
I would propose not to send the latter message to the site admin to avoid that admins don't know who also got this email / if somebody else already dealt with this.
I would also update the sentence at the bottom to if possible to make it clear why they get an email:
YYou receive this message because you are an administrator for the institution in which this person is a member. This is an auto generated notification from [site name]. To update your notification preferences, visit URL.
The same should go for Objectionable Content, and the virus messages. Though for the latter, the site admin should probably receive all emails.
There's also Bug 767569 that suggests some more granular improvements.