This made the rounds a couple months ago, and seems like complete rubbish. I've not read the book, but the only way I could get their numbers to work was to avoid intermediate steps when converting the amount of energy produced by area of land when I worked out the impact of the car.
In other words, the average year cost in energy of car, when factoring construction costs, equals say 55.1 gigajoules (10K KMs on a Toyata Landcruiser, which is remarkably fuel efficient btw). One hectacre of land produces 135 GJ, therefore you get about 2.5 cars per ha.
But when they did a dog they did not say that it uses about x GJs and therefore 135/x = dogs per hectacre. Instead they said that a hectacre produces Y amount of grain. A cow eats Z amount of grain. A dog eats C cows, therefore a dog uses C/(Y/Z) hectacres of land.
This is dodgy, since each intermediate step costs some energy not imparted down the line. (For example, not all of the cow is eaten by dogs, so we lose some energy right there.)
A more fair, although still very questionable, way to go about it might be to compare the amount of grain used for dog with the amount that could be used when producing ethanol. This has all sorts of pitfalls, e.g.
http://hir.harvard.edu/index.php?page=article&id=1911 (which interestingly states that filling an SUV requires 660 pounds of corn, or enough to feed to people for an entire year).
