In this sentence: "Tom is playing God of War at Tim's house."
The prepositional phrase "at Tim's house" works as an adverbial phrase?
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Yes, the prepositional phrases can act as an adjective phrase or as an adverbial phrase.
The girl with a smiling face is my sister.
Here, the phrase "with a smiling face" is a prepositional phrase in form and an adjective phrase in function.
Tom is playing God of War at Tim's house.
In your example, the phrase "at Tim's house" is a prepositional phrase in form and an adverbial phrase in function.
Tom is playing God of War [at Tim's house].
The underlined bracketed expression belongs to the class preposition phrase, and its function is adjunct.
Be careful, though, when using the term 'adverbial phrase'. It is potentially misleading since it is quite often used for any phrase functioning as adverbial and hence likely to be confused with adverb phrase (a phrase headed by an adverb).