The "third heaven" is a Hebraic way of speaking. The "three heavens" were what we would call the atmosphere (where birds fly), outer space (where the stars are), and heaven per se (where God and the angels and saints live).
I'm not terribly impressed with the theological quality of this article you post. (Not your fault -- it's the writer I'm not crazy about.)
For one thing, John Paul II never said that heaven wasn't a place. The Italian word he used was piu and, as any musician can tell you, piu in Italian means "more". He said that heaven was "more than" [just] "a place", that is, if we think of it as just a place, like Poughkeepsie, NY is a place, then we're trivializing it. Heaven is perfect intimacy with God; there are some people on earth who practically live in that perfect intimacy already, so their heaven has already begun here on earth.
Thank you. I've just had a moment.
Would that also imply that hell is complete isolation from God?