The funny thing is that most of these APIs wind up with what's essentially a "this" pointer at the front of every argument list so you're really doing OO anyway.
Do you have much experience with non-OO programming? Or even OOP, for that matter? How can one honestly believe that every instance of passing data into functions is automatically OOP? Did you even consider the fact that this has nothing to do with objects?
Time objects are a really bad example because time calculations are exactly the kind of hairy mess you want to hide behind some kind of abstract API.
You miss his point here. Time not being an object would not imply that it can't be abstracted into an API. Just see Clojure's clj-time library for an example.