This might seem like a throwaway joke, but I think it points to something very important. The characters are missing a commonality of experience that would enable each of them to understand the other.
Without commonality, only with effort can people understand another's perspective. Here, by each assuming the other is speaking in familiar terms, the characters are unable to communicate effectively.
Using Schroeder for this strip works because he's the character with the most dissimilar perspective of the kids. He's an artist, and his focus is a higher goal. This, I would say, is at the root of his differences with Lucy. Even Snoopy is more in tune with the other kids than Schroeder.
We still get strips in which Schroeder is playing ordinary kid games, but as the strip continues we'll see him doing this less and less.
