「あの、かりんさん・・・、そろそろお開きにしませんか？」「駄目、勝ち逃げ禁止！今度こそボクが勝つの！」

「、・・・、？」「、！！」

'Um, Karin... don't you think we should wrap this up soon?' 'No way! No quitting while you're ahead! This time I'm going to win!'

Literal

'Um, Karin-san..., soon [into-に] wrap-up don't-do-[polite-ません][question-か]?' 'No-good, winning-escape forbidden! This-time [for sure-こそ] [I-ボク][subject-が] win [assertive-の]!'

お開きにする is the standard euphemism for ending a party, game, or meeting — avoiding the inauspicious 終わる 'end' (which in wedding contexts suggests the marriage ending), substituting the metaphor of 'opening' the group outward for departure. 勝ち逃げ 'winning and fleeing' is a colloquial compound for quitting a game while one is ahead, common in mahjong and table games. ボク (僕) used by a female speaker (Karin) is marked, suggesting a tomboyish or playful persona. 今度こそ 'this time for sure' uses the emphatic particle こそ.