Not so much. The discovery and exploration of science is inevitable in any culture that is not specifically geared to stop that kind of freedom of thought.
What the author of that page failed to consider when writing it is that Christians were and are caught up in several of those intellectual traps; specifically the viewpoint that the heavens are 'divine', a tendency to deny the basic reality of the universe, and not being able to balance reason and philosophy. Also, the seventh argument he makes is incorrect. A culture does not need to view humans as qualitatively different (which is a very clear attack on the theory of evolution) for science to flourish; instead, it needs to be able to recognize the functional differences between humans and other animals, without putting humanity up on a pedestal of superiority.
Science develops not because of religious belief, but because of freethinking. That is to say, one of the reasons science developed further in Christian-dominated Europe than in the other places he mentioned is because it did not persecute freethinking as heavily as those other places tended to. Another reason is because European (and later, American) culture was not monolithic, although it did share a common cultural framework. A monolithic culture tends to hobble freethinking by its very existence, while cultures that are too different tend to impede its spread.
The main reasons the Greeks did not progress very far with science were that they were too divided against themselves, and they failed to grasp that experimentation was crucial to scientific development (which is why they got saddled with Aristotle's "four element" lunacy and certain other flawed ideas). It could have happened in Rome, if they'd had proper contact with India and China. As it stands, they had no external competitors and thus no impetus to push science, and they also had to deal with early Christianity, when it was at its worst and most virulent. Exactly the same problem that Islam had, in its own way.
But honestly, the real reason we have modern science is because although it got uprooted time and time again, it never got uprooted everywhere at the same time. Islam was able to carry the torch of science until Europe had gotten over the worst of its religious lunacy, and it served as a bridge whereupon Asian science and ideas were able to spread into Europe. And freethinking started to grow before Europe could get enmeshed in another fit of religious lunacy.