Dogs are pretty similar to humans, so it is quite likely that your dog has suffered no harm from this. Possible intestinal blockage and temporary constipation are possible, but unlikely to be life threatening.
Their quote about calling a vet is basically legal protection for them. To assert that crayons are non-toxic to dogs, cats, or other pets, they would have to put them through a regimen of testing to prove this – once for dogs, once for cats, once for rabbits, etc. These tests are expensive, and are pointless for the company – they are not likely to provide any new market or increased sales of crayons. So they don’t do it.
The manufacturer has to conduct tests and gain approval for each species that a drug is approved for. Since these tests are expensive, they will often not do this for less populous species, because they don’t see a big enough market to justify the costs of the testing.
But it’s common for Vets to prescribe them anyway. For example, our Vet sometimes treats our horses with a drug that is approved & sold for cattle, but was never clinically tested on horses. But horses & cattle are pretty similar animals, and many drugs work for both species. Such “off-label” use is fairly common, and equine veterinarians keep up to date on cattle drugs that have been found by experience to be safe & effective on horses.