Perhaps Matt Maranian could have checked over those plans one more time before mocking it quite so roundly. It seems pretty clear to me that the dog never comes in contact with the sheet metal... there's a soft flooring material (sponge rubber) between the metal and the dog.
There's also some sort of unstated assumption in the mockery that if submerged, the electricity feeding those 40-watt bulbs would somehow decide that the most efficient way to ground would be to travel up through the water to the sheet metal, somehow make it through the sponge rubber, travel through the dog, back through the sponge rubber, through the sheet metal, back into the water, and thence to the other contact in the bulb socket. Electricity only works like this if a) there's a hell of a lot of electricity, and/or b) you're a character in a video game or movie.
If you don't unplug it when the summer comes, you're not going to roast your dog. Dogs, traditionally, have these things called "legs" that allow them to move from a place that's too warm to a place that's less so. And if two 40-watt bulbs are making it too hot inside the doghouse, I'm guessing that conditions outside probably aren't at dog-freezing levels, unless those doghouse walls are made of some incredibly insulative material and the door is sealed shut. Remember, every time the dog goes in or out, a substantial amount of heat exchange will take place.
Yes, it's true that the plans have an implicit "we're assuming that you, the builder, are not a complete moron when you build, place, and operate this doghouse" attitude, but there certainly doesn't appear to be anything here that calls for this level of scorn.