。
I wonder if he enjoyed the last game.
Literal
He [topic-は] last [genitive-の] game [object-を] enjoy-did [conjectural-だろうか].
A reflective wondering question. エンジョイする is a loan-verb from English 'enjoy' — formed by attaching する to the loanword noun. Interestingly, Japanese already has the native 楽しむ for the same meaning, but エンジョイする is used in casual or modern contexts where the loanword carries a lighter, more contemporary tone. ~たんだろうか is the explanatory ~んだ (casual contraction of ~のだ) + the conjectural ~だろうか ('I wonder if X'). Together: 'I wonder whether [he really] enjoyed it.' The form is reflective rather than inquisitive — the speaker isn't asking anyone else, just musing.