I don't really see why you would have such a hard time with this one. You would have no trouble understanding me if I said 這是什麼樣的意思 (これはどういう意味ですか） instead of the standard 這是什麼意思 (これはなんの意味ですか）. It just happens that the former (これはどういう意味ですか) is how we word the question in Japanese and not the latter, although people would understand you just fine if you said これはなんの意味ですか.
どういう = どんな (although we wouldn't usually use the latter in this sentence)
Does that make it any clearer? That is, while in English we ask what the meaning is, in Japanese it is more common to ask what kind of meaning it is. I don't think this is a question of logic, and is simply a matter of convention. Both ways are logical.