Yes, a game is a great idea.

My friend has a degree in computing and statistics, working in climate change studies at Uni in the early 90's. Being a greenie he was disappointed that it seemed futile because, as you said, most people don't care about data.

He moved into electronic music thinking he could influence people with messages there (kind of like Simpsons embed messaging).

We now know that pop culture propaganda is somewhat futile in this regard too and if humanity does pull itself out of this mess it will be a vast combination of efforts in many fields. All of them seem futile in isolation.