The term "object-oriented" was coined by Alan Kay, and he did provide a much more precise meaning. Unfortunately, the term became a fad and was then diluted into all sorts of vaguely related ideas.
The page you link seems to indicate that Kay didn't propose this as a definitive definition of OOP, but rather as a description of the defining features of Smalltalk. I'm not familiar with the document; do you have any insight?
If you read this email, you will see that what he had in mind was much more than a way of programming. It was a model of computation where the computer is a networks of "cells" exchanging messages.
Kay's concept survives if you substitute "function call" for "message". Sending a message to an object and receiving a reply is closely analogous to invoking a function and obtaining a return value. Unfortunately, his overall model implies single dispatch. Sure, "everything is an object", but only one thing is the leftmost argument: the thing that receives the message; and the other things are just arguments.
Wow, just no. Sending a message to an object is more like calling your mom. Applying a function is like...applying a function. There is no real analogue for that, it's just math.
A function is well defined in mathematics; see http://en.wikipedia.org/wiki/Function_(mathematics) . Note that the definition doesn't really differ for computer science. Procedures, on the other hand, may or may not be functions according to whether they behave like them (match their properties).
http://c2.com/cgi/wiki?AlanKaysDefinitionOfObjectOriented
I find the original idea deep and worth thinking about.