How much of the total volume of the device was the case/housing?

I suppose the glue-everything approach is partly due to the desire of making a device very thin. There's no room for strong, load-bearing outer case, the internals are load-bearing.

You just need well designed rubber gasket. Thickness is impact resistance thing in those devices

It's been a long time, but the gasket itself was probably a millimetre or two thick, squeezed extremely tightly by the screws in the battery cover. It ran on AA or AAA batteries, and they took about about half or a third of the depth.