Yoko completely ignored John, and John for his part ignored her just the same.
Literal
Yoko [topic-は] John [object-を] completely ignored [and-し], John [possessive-の] side [also-も] her [object-を] same way-ly ignored.
し is the additive connective 'and (also)' — joins clauses that add/support each other. のほうも ('for one's part too') marks a parallel reaction. 同じように ('in the same way') uses ように as an adverbial 'in the manner of.'