No, that sounds dreadfully out of the ordinary; The pictures are horrifying. AxiDraw should pleasingly precise, with no appreciable play in the carriages.
The most likely case is that it got bumped hard during shipping, and bumped one or both carriages out of alignment. You should check for any more serious damage elsewhere (bent metal, broken parts) as well.
The good news is that it is relatively straightforward to tune it back up. If you write to us by e-mail (or use our contact form at https://shop.evilmadscientist.com/contact ), we can send you a PDF with instructions. If you read through them carefully, it should take you about five minutes to get back to AxiDraw-level precision.