Answer: The word 'climbing' is a gerund in "The children enjoyed climbing on the playground equipment".
Explanation: A gerund is a non-finite verb form which functions as a noun. Moreover, a gerund can play different syntactic functions in a sentence: it can act as subject, as direct object or as object of the preposition. In the sentence "The children enjoyed climbing on the playground equipment", "climbing" is a gerund since it is functioning as a noun and acting as the direct object. In contrast, in the other two sentences, "climbing" is a present participle.
