Looking at the pictures, how level the floor is has little to do with the bowing of the top of the stand. That is due to the strentgh of the cabinet's materials (probably chipboard, like most kitchen cabinets in the UK), the spacing of the vertical supports and the compressibility of the leveling mat.
Putting ply between the cabinet and floor WILL NOT stop the upper "shelf" from bowing.
Putting a sheet of 12mm (or 18mm) ply between the tank and the cabinet might.
Whether replacing the leveling mat with styrofoam would make much difference is debatable, as they both do the same job.
Whether the bowing is something to be concerned about is also dificult to say.
Once you start getting away from the four fertical supports, the upper "shelf" provides almost no support for the tank. All the load bearing is in the vertical pieces. By deforming the upper "shelf", the vertical supports are pulled slightly together, which moves them slightly off plumb, and therefore acts to reduce the cabinet's strength. But the deflection will be very small, and probably of a similar degree to manufacturing tollerances and possible that cause by environmental factors. So whether it is significan is unknown.
The floor does look pissed, but not in a way that will cause the bowing shown, and it may be down to the camera angle anyway.
If you want to find out if the floor is level, you're better off putitng the spirit level on the top edge of the tank itself, as the glass will not deflect significantly, is more likely to be perfectly straight, and will give a reliable datum for the horizontalness of the cabinet. (It also won't matter how long your spirit level is.) However, it will only tell you how level the floor is between two out of the four verticals are, and it won't tell you which.
The biggest question for me is whether the stand was built for that tank, and by the same company?
If so, does it have a waranty?