The word group that contains a subject and verb in agreement with each other is "contestants are running".
A word group is a group of words where there is a grammatical relationship between the words. In our example: "contestants are running", the subject is "contestants" and the verb is "are running".
The agreement rule that applies to a subject joined by or nor is: use a singular verb. A compound subject, i.e. a subject that has more than one item in it, and consists of a choice, for example, "The cat or the dog ran after the mouse." The compound subject in this sentence needs a singular verb.