If you have some US dollars and are considering investing in Apple stock, you don't take the price of oil into account (unless you're also considering investing in oil).
In the same way if you have Bitcoin and are considering investing in SDICE, you don't take the price of US dollars into account (unless you're also considering investing in fiat).
Apple is not denominated in oil, or it would have to be taken into account.
If the Bitcoin economy holds $1,000,000,000 of wealth at 11,000,000 units, each bitcoin is worth about $91. Assuming SD is worth $10,000,000, that would make the business worth 110,000 bitcoins.
If the exchange rate doubles, making the Bitcoin economy worth $2,000,000,000, but SD remains at the same absolute valuation, it should then be worth 55,000 bitcoins.
SD has been estimated to be worth $100-200,000,000, which I think is appropriate. This means that at a current economy size of $1 billion, SD should be worth 10-20% of the entire stock of bitcoins, or 1.1-2.2mm BTC. Therefore, the share price should be about 3-6x higher than the 0.0033 level. Hypothetically.
Of course, there are other factors, but that shows the USD relation due to both it and Bitcoin being concurrent measures and stores of value.