It still has to move very fast. The problem is that the laser projects a dot. If you want to see an image or test, you have to move that dot across the surface so fast that the human eye doesn't realise that it's actually just a moving dot.

Think about how a CRT monitor works, with the electron beam scanning across the rows. On a 60Hz 640x480 screen that requires a scan line rate of 28.8kHz (ie scanning 28800 lines per second). This is a bit easier than the Peachy's job because the phosphor in the screen has some persistence (it stays lit up for a while after the beam hits it) so you do only need to scan at 60Hz. Without that phosphor (which the Peachy obviously won't have) you're relying on the human eye's own persistence. It appears that to use this well you need to run at 100Hz or so.

Now you have to find out how many lines are needed. Say the Peachy projects a dot 5mm across (when the target is a wall a few metres away). If you want a display 2m high then that'll be 400 lines. 100Hz and 400 lines is a 40kHz scan rate - you have to be flicking the beam back and forward 40,000 times per second. So, even for static text, the beam needs to be moving seriously fast.

My understanding is that the proper laser projectors manage this by having the beam oscillating back and forward for the scan lines, which allows for very high speed without needing complete actuation. They probably also use much larger dots to cut down the number of lines.

The Peachy isn't built for this sort of use. It's designed to move slowly (relatively) but with a lot of control over position and velocity. It's almost certainly designed not to oscillate, because oscillation makes control much harder.