I don't think anything that complicated fundamentally is taking place here.  When the exchange rate was roughly flat or a slow increase, SDICE was a nice way to increase your BTC holdings, especially as it corresponded with the news reports about SDICE's earnings in 2012.

However, as the value of a bitcoin increases rapidly against the dollar, it is a bad idea to hold it in SDICE.  I have lost 28 BTC (market value of over $1300 at today's price), in a couple of months, while getting dividends of 1.7 BTC.  Had I simply held onto my bitcoins, those would be worth $2300, while instead my shares + dividends are worth $1000.  Holding a stock denominated in BTC greatly increases your risk (stock price can go up or down, as well as the value of the BTC it's valued in), so it primarily makes sense in a stable exchange environment.