Quina's motive for joining the party is not out of a desire to save the world (at least not until s/he is eventually made aware of how high the stakes are), but rather as an opportunity to taste different foods from all around Gaia. As a result, s/he does not hold a particularly high interest in the dramatic events that unfold during the course of the story (unless food is involved somehow), but nonetheless fights hard alongside Zidane and the rest of the party to achieve their goal of saving it from Brahne, and then from Kuja.