It is ths stimulant theobromine that is toxic to dogs. Basically, it affects the heart, causing it to speed up or beat irregularly. This is what can make the dog ill or even die if it causes the heart to stop. Exercise can bring this on.

If the human body didn't expell it faster, the same would probably happen to us too.

Milk chocolate is still dangerous to a degree but a dog can eat more of that than dark chocolate to be affected by theobromine poisoning.
I have heard of dogs get ill or even die just from eating some milk chocolate too.
I read about two english bulldogs who died within minutes of each other half an hour after being fed a piece of sponge cake with a bit of chocolate on top. They were champion showdogs too. The owner had several more and was a breeder but, feeding their dogs crap like that, they weren't very responsible with regards to diet and every dog owner should know about the dangers of chocolate but some people refuse to believe it because they always fed their dog chocolate and it didn't do anything to it yet.....

The owner of the bulldogs stated how the male dog that died had been fed a bar of chocolate every evening all of his life, he was 7, and it had never done anything to him before. What idiot feeds their dogs a bar of chocolate every day?