。
Let's keep playing the game after dinner.
Literal
Dinner-after, again game [object-を] continue-[plain-volitional-よう].
続けよう is the plain volitional of 続ける ('to continue') — the casual 'let's' form. また ('again, also, moreover') here just means 'again,' anchoring the continuation. The sentence is a natural friend-to-friend suggestion, probably between kids or gamers. Note that 続ける is transitive (takes を), distinct from the intransitive 続く ('to continue, to last').