There is a participle phrase in this sentence. Participles and participle phrases act as adjectives, meaning they describe someone or something.
"Staring up at the gigantic water slide" is a participle phrase describing Max. The specific participle is "staring," and the entire phrase is "staring up at the gigantic water slide." (We know "staring" is a participle because it is a verb that ends in -ing and is being used to describe something.) The entire phrase is describing Max, who is the subject of the sentence.
There is also an infinitive in the sentence. The infinitive "to play" appears at the end.
