Does this imply that the all plastic gamer PCs (that are more designed to be art projects than serious computers) are bad and that everyone should be using systems with solid steel cases to block radiation?

Plastic cases might actually be a bit better than steel depending on the radiation type. Neutron radiation is more effectively shielded by interacting with light atoms so stuff with lots of hydrogen atoms like water or polymers have a better chance of interacting with neutrons and slowing it down so that it can be stopped. Steel is probably better for gamma radiation or charged particles like muons.

But overall, pc cases are probably too thin to appreciably affect the radiation levels. Cosmic rays and their secondary radiation is fine with going through buildings so a 1mm thick case isn't going to do much.

A steel case has too little effect on cosmic radiation, but it is good to shield electrical noise.

The computers in plastic cases can sometimes be affected by appliances with electrical motors that are used nearby them.

The cosmic radiation is attenuated only inside a big building, e.g. one with many stories above you. A really great attenuation is obtained only underground.