I read the title of your post and I couldn't help but think of the movie Arrival. Hopefully you've seen it or that might be a spoiler. Whoops! Anyways, language influences culture so much and I'm glad you drew that connection here. In designing new systems and products to avoid plastic waste, the proper language to even explain the problem and its solution will be essential to it taking off.
Looking at this problem through the lens of gamification is a great way to do it! I think a social media aspect would be a crucial part of any game, but could help motivate people to participate. The participating recycling infrastructure would also be very important. Is there current collection infrastructure is in place that could potentially be piggy-backed off from?
I really like this! Where I live there is a high bottle deposit, and yet sometimes people are still to lazy to return the bottle or find recycling for it. If they knew they could get the instant gratification for their good behavior, I wonder if that would help recycling rates even more.