The corner damage doesn't look too bad. The good news is that it is plywood.
If it were mine to fix I would approach it this way:
1. Go to the local drug store and pick up a few large needle diameter syringes. As bad as that damage is, you'll need to inject glue way up in between the layers. I personally would use
white Elmer's glue as it has longer open time and very similar hold characteristics as wood glue.
2. I would cut a 12" wide piece of MDF or plywood that would fit tightly in the bottom against the bottom board. This board would support the edges that hang down, helping to compress them under clamping pressure. I would wrap the edges of my board in packing tape, so I didn't glue it to the machine.
3. Looks like a set of bar clamps or pipe clamps will be the best. Use a block of wood to distribute the pressure over the damage - this will give the flattest finish repair. The block needs to be flat and true and i would cover the face with that packing tape again (wax paper also works, and might be better for preventing tape residue from getting on the sideart)
4. I would clamp across the front and across the bottom, trying to get even pressure across the block. F-type bar clamps would be best - they have a little more "leg" length so you can reach further away from the edge.
5. I would do a couple dry runs. Make sure that the pressure goes where you need it, the plywood closes nicely, etc.
6. Inject between the layers with glue (syringe

) and clamp, keeping the glue off the art with a damp rag.
7. Wait 24hrs and remove clamps. Play a game

Oh... BTW, nice TZ!
Dave.