All the laser pointers I have seen, are in fact lasers. It's easy to tell, If you point one at a wall about 20 feet away, it will create a very small point of light, a few mm across. If you do that with a LED light, the beam, if it's powerful enough will be anywhere from half a meter to a meter in diameter. Only a laser can keep a beam that tight.
The device you link to is a real Laser
There are laser Diodes, which might be the source of the LED comment. Here are some commercially available laser diode modules.
Small, inefficient lasers are cheap. They're used in DVD players, CD players, bar code readers, and in the mouse I'm using.