Answer:
The infinitive phrase in the sentence functions as the object of the verb "want".
Step-by-step explanation:
Infinitive phrases are groups of words comprised of a verb in the infinitive form - to + base form - and any modifiers related to that verb. Infinitive phrases can function as nouns, adjectives, or adverbs in a sentence.
In the sentence we are analyzing here, the infinitive phrase is "to play for our team." It functions as a noun in the sentence, more specifically as the object of the verb "want". What does John not want? To play for our team.