Wow, never seen one as bad as that!
To be honest you're lucky to have one that throws a clay at all.
Normally you would expect a clay to be thrown straight away from the trap if everything is set correctly. If it's spitting them to the left it's being dragged by the rubber, if it spits it up like a teal but straight ahead it's being pinched towards the end of it's flight off the arm. However to spit it off the left and send it airborne wobbling...certainly different!
You're saying the clay slides easily up the arm underneath the rubber, you should have 1-1.5mm of air between the bottom of the rubber and the top of the first ring of the clay. This has to be right to the tip of the throwing arm. I would expect the rubber to be fully in contact with the rubbed driving band of the clay through it's launch.
Looking at the flight of the clay in the video, there's no life in it...it doesn't look like it's getting any proper spin imparted to make it fly straight. Question is...is this due to lack of grip on the rubber, or is the throwing plate distorted? The clay looks like it's being flipped up, so could be an out of square arm.
If it's brand new I'd send it back, get a refund and then go find a decent second hand Laporte, Bowman or Promatic.