The unit price looks low but the cost driver in these apps is usually the context window. You have to re-send the full history every turn to maintain state, so you end up paying for the same tokens dozens of times. By the end of a long session the cost per interaction is significantly higher than at the start since you're re-processing the entire game log for every new command.

Cached tokens are cheaper. Also there are ways to compress the context (not sure if this game employs any of those techniques).