The space shuttle certainly appears plane-like; it has the same general shape, and it flies. However, the shuttle is not an airplane according to the definition of the things you see at the local airport.
A true airplane, such as Amelia Earhart's, can take off from the ground under its own power, maintaining lift due to the shape of its wings, and control its course through the combination of flight controls (movable parts of the aircraft that change airflow) and continued use of its own power.
The space shuttle was actually a system, and what most people think of when referencing the shuttle was called the orbiter. This was the black and white portion that looked like an airplane and housed the crew and any payload being carried to space. The orbiter was not capable of true flight; it was designed as a glider. The orbiter was incapable of taking off from a runway for several reasons: its wings, for example, were designed for gliding and heat dispersal, and the amount of fuel required to put the shuttle into orbit was several times the weight of the orbiter itself.
However, just because the shuttle wasn't technically an airplane doesn't mean that the statement in the article is incorrect. Since the phrase "the sky is the limit" is usually taken in a metaphorical context, and the article is attempting to phrase it literally, the statement can be supported by the fact that space is beyond the sky, and many people would colloquially consider traveling to space to involve "flying" in the same sense that atmospheric flight does.