That's because the only actions you can take in the game are "buy the index" and "sell the index".
As soon as there's more than one price in the market (even, say, one index tracking DJIA and another one tracking S&P 500), it's possible to beat the market average while prices are rising.
I'm not saying you can do it without knowledge of the future. I'm responding to the (correct) observation above that it isn't possible to beat the market average while it's rising, no matter what you do, even if you do have knowledge of the future -- as long as the only options you have are "buy the index" and "sell the index".
I don't get why is beating the market a goal, isn't making money the goal? I am much happier making 20% while market is up 30%, than losing 5% when the market loses 20%.