First off, to my knowledge so far they haven't sent any profits to any shareholders. And secondly, if they do start paying dividends, they could just be paying them from the principal/IPO cost of the shares. Then its in their interest to keep doing so, as long they issue and sell more shares.
The SatoshiDice operator(s) can use the house funds to simulate players and revenue, obviously at no risk. Whether there are investors or not has no effect on the possibility of inflating players and revenue by simply generating a bunch of transactions to the SatoshiDice addresses. However, if they are raising funds from investors or trying to sell the business (and they are), then to inflate revenues is clearly in seller's best short-term greedy interest. They don't care about the long-term viability because they're selling their stake.
They have paid thousands BTC for dividend: http://mpex.co/?mpsic=S.DICE
Maybe it's just a pump-and-dump trick. Not only the players are fake, they also pretend to be investors. They may just buy 90% of their IPO so the actual dividend they paid is minimal. By pumping the profits, they can sell their shares with very high premium. When they have sold most of their shares, those fake players will disappear.