Title text: Why would anyone ever, ever say that? Please, nobody ever say that.
One-upmanship is the act of surpassing another person. In this case, one female character is one-upping her friend's claim of being taken on a mountain hike with a claim that she was proposed to.
Mario is the star of the Super Mario series. In the games, completing specific conditions causes a "1-up" to appear on screen, referring to an additional life. The comic relies on the homonym of the action of one-upmanship and the event of one-ups in Mario.
Randall in the image text seems to imply that he finds it a pretty bad joke.
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