It's not laser tagging, because otherwise you'd see the laser point.
A friend of mine does this just with Photoshop and a Wacom tablet/screen.
You can also use Modul8's Paint module

ms-paint and a mouse?

Could be something like laser graffiti -

http://graffitiresearchlab.com/projects/laser-tag/

I think laser tagging is more advanced than whats going on in the first video.

But it's a similar concept.

hdmi out from an ipad/tablet to a nice overhead projector, i bet...  or some sort of video out

Just output any app you can write on to the screen? I don't see any science behind this.

Seems very simple... possibly something you could set up with an iPad or a Wacom tablet? Both things I have...