What he's talking about is a futures market -- a legal way of speculating on political outcomes. Later, you can sell it, based on how the stock moves, or you can get the payoff at the point where the outcome is certain. So, let's say they were each at $5. If you bought one of each (one bet on Romney winning, one on Obama), then after the election one would pay out at $10 and the other at $0. You'd make nothing. In fact, after accounting for short-term capital gains and the cost of the trades, you'd lose money. But, let's say Romney's at $4.12 and that's the only one you buy. If he wins, it pay's $10. You more than doubled your money. Even after accounting for capital gains and trading price, you could make a serious killing on it. It's like taking the underdog in a sports bet.
Where it arguably differs from sports betting, is that it's meant to be a hedge... a bit like weathers futures, or commodity futures. If Romney gets elected, it's bound to have certain consequences on other things.... for example, it would probably help business for certain businesses that are in good with Romney, and others that tend to do well under Republicans generally (like Halliburton or polluting industries or defense contractors). So, if you have a lot of holdings positioned to do well if Romney wins, you could buy stock in an Obama victory, to offset your loss if Obama wins. Or, on the flip side, if you own a lot of things expected to do well if Obama wins (like green-energy-company stock), you could buy stock in a Romney victory, to offset your loss if that happens. So, it's not exactly gambling. But the great thing is that it acts as a reality check on all the media blather. The media can act like a particular political outcome is all but certain, but if it really were certain, the price would be about $10 for the stock, since there'd be almost no risk for the investment. In the case of Romney, right now the people who are putting their own money at risk, rather than just blowing hot air, are indicating an assumption that Romney is likely to lose.