It has an expiration date, but I think all consumables have to have one. Even water, which should last indefinitely if stored properly has an expiration date.
Seeing how Listerine is just a collection of 5+ antimicrobials and there is nothing for microbes to eat in there (that I know of, it is a calorie free liquid other than the alcohol which would be toxic to microbes) I would assume a bottle becoming full of pathogens is not an issue. Even if they survived all the antimicrobials there is nothing for them to consume for energy.
Do products like Listerine have an expiration date because chemicals from the plastic bottle can leech into the Listerine itself? Is it because the main ingredients can break down over time? Or is the exp. date just randomly chosen?