Need to understand how this rule is defined in the attachment. Does the item[ ]

The answer to your original question, I think, is Yes - the first instance of "item" should actually be called as "ri!item" in the rule. But i think it'll work without that, confusion aside.

The simplest way to demonstrate this rule would be to call it from another expression rule. Since ri!item is of "Any Type" type, you can't actually force in an array when you use the "Test" functionality in the expression editor. But if you create a new / unsaved expression, you can pass in an array. Such as:
rule!CASE_APP_randomItemFromArray(
{ "first", "second", "third", "fourth" }
)

The answer to your original question, I think, is Yes - the first instance of "item" should actually be called as "ri!item" in the rule. But i think it'll work without that, confusion aside.

The simplest way to demonstrate this rule would be to call it from another expression rule. Since ri!item is of "Any Type" type, you can't actually force in an array when you use the "Test" functionality in the expression editor. But if you create a new / unsaved expression, you can pass in an array. Such as:
rule!CASE_APP_randomItemFromArray(
{ "first", "second", "third", "fourth" }
)