"John" and "Mary" are each simple subjects -- subjects without any words describing them. In order for it to be a complete subject, there would have to be modifiers. If the sentence said "Big, hairy John and sweet, pretty Mary run," that would be a complete subject. In fact, it would be two complete subjects!
Here, though, you have no modifiers. Don't be fooled by the fact that the subject includes more than one word. You can have a simple sentence with two subjects, like this one.
Think about it like this: this sentence is like two sentences squished into one. "John runs." "Mary runs." In those sentences, there's no doubt that the subjects are simple. Those subjects haven't changed in your sentence, so they are still simple subjects.