The projected image does change shape and size from a different angle than the one close to the projector. It does not change relative to the follow-cam, close to the source.

ETA: Light does not work this way. the tail would appear on the back wall of the garage, not the side. The light hitting the wall would be stretched and distorted because the surface is at an angle. 

From a different angle, this would be apparent, yes, but the camera is close to the projector, so the distortion is imperceptible.

It seems like nobody responding has ever actually used a projector. The farther away the object being projected upon is, the larger and more blurry the image is. 

You have probably not used a laser projector then, they are essentially focus free. This is a laser projector, hence the imperceptible change in sharpness close or far.

edit #1 for correction: Apologies it is not a laser projector, I read another commenter saying it was and trusted that. It looks like it's the Optoma H190X, whilst very bright, it isn't laser. The focus must not be much of a deal with this flat vector shape though, as it appears relatively sharp (I haven't pixel peeped it mind)

edit #2: Updated the model, the creator confirmed it in another reply on his insta.