Answer:
No, "I enjoy running" does not have a direct object.
Step-by-step explanation:
A direct object refers to the noun or pronoun in a sentence that receives the action of the verb. In a sentence with a transitive verb, the direct object answers the question of "what" or "whom" the subject performs the action on.
In this sentence, "I" is the subject, "enjoy" is the verb and "running" is not a direct object because it doesn't receive the action of the verb. The sentence is a subject-verb-complement sentence, the verb "enjoy" takes a subject-complement clause to complete its meaning, the complement clause is "running" indicating the thing that the subject finds pleasurable.