Guess she realized she couldn't win, she'd already lost before she started playing.
Ultimately, that's the point. Kamiya was of course well aware of Minami's feelings for Yuzu, but if Yuzu didn't reciprocate those feelings, Minami's crush would ultimately be hopeless and thus leave a window of opportunity for Kamiya. However, seeing Yuzu's reaction and thus realising clearly that she's also got romantic feelings towards Minami, Kamiya can do nothing but give up, there's just no angle for her here.
Of course, one can criticise this as being just an expression of the trope where a convenient rival appears just at the right time of the story and then disappears again quickly, but in character it actually makes perfect sense for Kamiya to give up at this point, the more unrealistic part being her not being present as a love rival from the start.
Ultimately, I think that this series doesn't take itself too seriously and clearly follows tried and tested romcom patterns, so being a bit tropy is honestly par for the course.