The blockchain is a system for transferring value, of which the final total is specified in advance. Those are the terms of the social contract every Bitcoin holder has adopted understanding. Those are the terms every node has agreed to voluntarily participate in the network.
Nodes and miners have not unanimously agreed to have their resources/time spent inefficently processing informational messages like "you lose", "you win", or even "I bet on game with much". This was never part of the agreement.
Would the latter two of those "messages" not represent a transfer of value, of which you just stated that Bitcoin is a system for? I presume (I haven't looked at exactly how Satoshi Dice works) that when you place a wager, the player is transferring value to Satoshi Dice. Then, if they win, Satoshi Dice is transferring value back. I see no transfer of value in the "You Lose" message as I would assume Satoshi Dice keeps the value, so I completely agree with you there, that would be a completely informational message.
While there is a value attached to the latter two, it is
primarily a message. Otherwise, a gamer would just transfer a deposit, play, and withdraw (as I notice your site does) - no message passing involved.
For an easy analogy, this would be like WalMart charging your credit card for every item you pick up off the shelf, and refunding you if you put it back (actually worse, since SD uses 2 transactions for every action).
Not even VISA/MC could handle that kind of abuse, and their system (being centralised) is
far more efficient than Bitcoin.