How can a Boeing 747 take off from Princess Juliana 7,546 ft runway?
(Source: Boeing)

The approx. 10,700 feet Wikipedia figure is for a fully loaded 747 at sea-level. The lighter the plane, the less runway it needs. The 7,500-foot runway at TNCM allows a takeoff at 84% of the maximum takeoff weight. (Not taking into account any climb restrictions, such as the big hill over there.)

And as Terry pointed out, "ambient temperature also enters in. The cooler the air is, the more you can lift." And vice versa for a hot day.