Yes, it's just a dumb TV show, but in this case we see the laws of economics accurately portrayed: once the castaways realize they're marooned indefinitely, their economic thinking focuses on the limited resources of the island. As Mises claimed, any fixed amount of money is the correct amount of money for a given economy. Prices will adjust. If the supply of gold money is high, and the available goods and services are few, then prices will be very high in terms of gold. And in this context, the gold money supply isn't fixed: the mine is still there, with who knows how much more gold yet to be extracted. Under an island gold standard, the supply of money might increase at any time, and anticipation of that fact will drive current prices still higher. The money ends up heavier than the goods it trades for.
The government paper in Howell's suitcases, on the other hand, is easy to transport, hard to counterfeit, lighter than gold, and whatever amount of it the millionaire managed to bring with him is the amount there's going to be for a while.
On this isolated island, and in this isolated context, paper beats gold.
Yes, I know, it's not possible for me to be any more of a geek...