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Sleeping in airports is not uncommon when transiting through. Quite a few people stretch out and nap while waiting their next flight. But this is primarily in the transit areas, security often frowns on folks sleeping in the public area around the check in counters (otherwise homeless folks would flock to the heated airport lobbies armed with a second hand suitcase).
Both the Mecure Schipol and Yotel are inside the international transit area, so you can't access them until you check in for your flight. The Yotel was closed last September during renovation, not sure if it has reopened yet.
The best bet is to book one of the other three on that website, since they are all within walking distance. Or look on a booking website like Agoda and pick a hotel that offers free airport shuttles.