。
'Let's play baseball,' he said.
Literal
Baseball [obj-を] do-[volitional-しよう][invitation-じゃないか][quotative-と] he [topic-は] said.
しようじゃないか ('let's do it, shall we?') is a casual, slightly insistent invitation — the volitional しよう + じゃないか ('isn't it?') stacks two sentence-ending pieces to create a rhetorical invitation. The quotative と marks the end of the quoted speech before the main verb 言った.