"Fast and slow dogs happily played at the dog park, and the owners talked eagerly".
If by "adverbial phrase" you mean a phrase that has an adverbial function, i.e. one that modifies a verb, then the underlined elements are adverbial phrases: they are phrases that have an adverbial function.
Many modern grammars do not use the term "adverbial phrase"; instead they use the term "adjunct". It avoids confusion arising between "adverb phrase" (a category of phrase headed by an adverb) and "adverbial" (a function that can be realised by several kinds of phrase, not just adverb phrases.