How to create a rule to notify administrators of new comments by non-administrators?
What you are trying to do is pretty straightforward. I suspect that you have a Rule that is active and has the following:

On event After publishing a comment

(no condition)

DO

Send an email to user (or whatever you want to be your notification method; it doesn't really matter)

What you need to do is add a condition by clicking on the respective option. In the "Condition to add" option, you need to select: "User has role(s)" and press Next. 

In the next page, select "Published Comment Author" in the User option and select all the roles of your site except for the Admin role. Leave the rest unchanged.

Now your admins should be receiving notifications for comments from non-admins only.