There are some traits, like short bobtails, where variation in one gene is enough to predict outcomes. Since dogs (like most animals) have two copies of a given gene, you only need to track three combinations, or genotypes (e.g., AA, Aa, and aa) for these traits. In contrast, there are other traits, such as height in humans, where variation on thousands of genes is needed to account for the outcome on the trait. The number of genotype combinations then is very high, and most of the underlying genes are not even known. You can't predict anything when you don't have predictors!
When it comes to size in dogs, and in particular breed dogs, the reality is somewhere in the middle. While more than one gene affects the size of a dog, fewer than twenty genes explain almost all of the variation in purebred dogs. This is due to the particular history of breed dogs, where much of the variation that might otherwise be present is gone because of generations of selective breeding - it's easier after all to select for a gene for huge (or tiny) dogs than one for very slightly larger (or smaller) dogs. This results in the huge range of sizes we see, from the Chihuahua to the Great Dane, which dwarfs anything we see in human populations. But even in very mixed dogs from villages in Africa and Asia fewer than twenty genes can still predict almost half the variation in size!
When your dog is genotyped all of the markers that are useful for prediction are on the Embark chip. Using the results for each given gene we add or subtract from the final predicted adult value for a given dog. Size is one of those traits where genetics can be thought of as a rather strict blueprint, as long as the dog has nutritious food and no (technically, "not too many"...but if that grosses you out, think "no") parasites as a puppy. Genetically testing your dog basically allows Embark to fill in the details of the blueprint even before your dog grows into its paws.
In the future as we collect more data and get feedback from customers we anticipate that our predictions will get even better. Ultimately the goal is to give dog owners the very best predictions for their pup so they can make the best decisions for their future together.