(Animator here) You have to back out of the arcade machine and exchange the tickets with the counter cat -- unfortunately we ran out of time before we could make that flow more obvious :/
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Ok thanks. Gosh, sorry, now that I've beaten the rat I can't figure out how to get two tickets to exchange for the second boss fight. I've tried doing the rat and the tutorial multiple times. I was actually getting excited... lol. Wait. Somehow I started getting tickets. Okay, this game is cool! I can't seem to get a high enough score on the rocket rat, but I feel satisfied with this game now. Thanks for the good time.