EDIT: Neil! Don't butt in!
Ok - this is a bit tangled up. Let's see if I can pick it apart for you!
Firstly, the rectangular notation for a Use Case did originally show the <<use case>>, but that is not a stereotype, it is a keyword (and not a keyword you type into the Properties dialog either). Use Rectangular Notation on an Actor and you will see the keyword <<Actor>> on that.
Secondly, Rectangular Notation makes the other elements look like Classes, so we added - for example - the keyword <<actor>> to indicate that this is an Actor element, not a Class.
We don't add the <<use case>> keyword any more, because we have a nice little icon of a Use Case in the corner of the element to show what kind of element it really is. We still use the <<actor>> keyword because we don't have an Actor icon in the Rectangular Notation version of that element.
So, the Help topic needs to be cleaned up, because it harks back to a period when we used both keyword and icon in Rectangular Notation of a Use Case.
Did you actually type "use case" into the Stereotype field of the Use Case element Properties dialog? Unless you have defined that stereotype to do something, it will only act as a label on the element.
The <<Activity>> stereotype, on the other hand, is defined in BPMN and it redefines the element shape, so if you add it to an Activity it automatically applies the BPMN Activity shape.
You should find (in recent releases of EA at least) that if you simply create a Use Case element and an Activity element and apply Rectangular Notation to each one, they both become rectangular cells with the element name at top center and a small icon in the top right corner. And with no keyword text in angled brackets!