。
He went out in spite of the storm.
Literal
Storm [to-に]-nevertheless he [topic-は] went-out.
にもかかわらず is a formal concessive ('in spite of / despite') that attaches to nouns via に and to plain-form clauses directly. 出ていった uses the ~ていく auxiliary, indicating motion away from the speaker: he 'went out and away.' The entire sentence has a written, almost literary feel.