Does "pride" mean "prize" in this context? Because the phone number of Rosa's friends in the next fragment seems to be a "prize" for me.
That's a good guess! But the speaker does intend to say "pride" here, as he is expressing that pride is what motivates them to play. They dislike losing, hence why the speaker says "we play for pride." Ex: His sense of pride didn't allow him to reject the challenge. Ex: The team is motivated by pride.