My guess it is a short pulse laser, These lasers can reach very high intensities- a high enough intensity in air can strip the electrons from the air molecules and create a plasma- very similar to the plasma created by lightning. Its hot and it glows like lightning.

You can project a beam that doesnt have the intensity to cause formation of a plasma, then use a lens or an adaptable mirror to bring it to a focus- by adjusting the intensity and focus you can control the position and size of the 'spark' created at the focus. If you vary the position of the focus then you can write in air...

I did this all the time- never drew pictures with it, I thought it would be cool to try but the equipment would have cost a bit... and there is the laser safety issue.

Once, with a 1500 Watt short pulse laser, I brought it to a focus in air, I asked an assistant to watch as I turned up the intensity and tell me when it started to create a plasma- I, of course, made sure that all safety measures were in place.

I turned up the intensity and and finally at one point there was a loud sustained 'BRAAAAAAAAAP!!!!', the assistant yelped and I shuttered the laser and ran to see if he was ok, he had leaped about 10 feet away but was only startled. The laser had created a stationary 'lightning bolt' about 8" long that created a VERY loud noise.

A display based on this would have very limited applications- first off there is no color- at least the way it is- second, there is a real safety issue, and third- creating an image at a great distance is not practical, to create a sharp focus at a large distance requires a big lens... This has some applications, sure, but it isnt useful as a 3-D TV set, its a neat and sophisticated application of a known phenomenon. It would be annoyingly loud.