The funniest thing from our baby years is that rather than try and copy adults (as kids do and that is how they learn to walk) we were quite happy just copying each other, and so ...
Yes, this is exactly the thing. Twins have someone to copy who approves of their choices and understands them, so that is how their language and games can develop which no one else understands.
My twins did not have a totally separate language, but they would make up words for the people and things they liked most, like close relatives, Disney characters, animals, and, as I recall, Christmas lights! They knew what the real name or word was, but they chose to use their own instead, and we didn't discourage it. The funny thing was, they would use these alternate names so much, that my husband and I would start using them, too, and then forget when we were speaking to others that they wouldn't know what we were talking about...LOL.
--Maria