The traditional two-party result in Game Theory makes the assumption that voter preferences lie on a linear continuum. So given any two people, one will be more "left-wing" than the other, and you can find some moderate in between. Parties then jostle for the median voter, and political dominance is unstable.
In reality, the political landscape tends to be more broken up. You have issues like abortion which cleave the electorate. With large population areas, such large Democracies, there tend to be sufficiently many issues that the two parties take on many differing positions and you can effectively think about a "marginal voter" who is torn about which policy preferences should receive greater weight. So any political dominance is always unstable, as the other party can create enough wedge issues to come back.
The problem in smaller political units is that voters are split on fewer issues. Voters tend to be much lower information on local races and go with identity more often. In Chicago for instance, the Daley machine can get at least 60% of the vote in primaries from their vote bank of Irish, immigrants, and other whites. It's hard to compete as another Democrat (let alone a Republican) since Daley serves his base very well (plenty of union and city jobs), and his base is over half the Democrat primary pool. Add to that the fact that city dwellers tend to have relatively uniform social preferences on issues such as abortion, gay marriage, teaching evolution in school, etc.
Similar ethnic divisions are at play in Singapore (Malaysia too). With a large Chinese supermajority, the Lee family makes sure to reward their supporters well. South Africa displays this pattern too, with the ANC commanding the undivided support of a large black base (though high-profile splits in that party might be important).
Explaining this paradox is all about showing why a competing party can't arise in small places while they can in large ones. If you can get >50% of the population to care about a simple set of issues, and then become the best person at providing them with their needs, you have a stable dominant equilibrium even in a democracy.
More interesting perhaps is explaining the long legacy of one-party rule in large and pluralistic democracies like India, Mexico, Taiwan. There the answer also has to do with the costs of building a political machine, and the use of state coercion to tackle political opposition, as well as reputation buildup in the freedom struggle (in India). Information costs in large democracies mean that the scions of politically powerful families start with a heavy stock of reputation capital, explaining the prominence of political dynasties in South Asian Democracies (Gandhi, Bhutto, Zia), and also American and Japanese Democracies.
This is also why you see a greater share of female political leadership in some foreign democracies than in America. In the US, political leaders tend to be drawn from the stock of well-connected lawyers (which is largely male), while in other countries leaders are often drawn from certain families (which are, presumably, half female). Hillary Clinton's rise was only possible from her position in the Clinton family, and Pelosi too is politically well-connected. Just like female rule in those countries, the rise of female politicians here is more a dynastic victory than a feminist one (just like how Queens Elizabeth and Hatshepsut didn't really advance women causes either). People like Merkel, Thatcher, and Mayawati seem like better signs of social progress. But it's also seems easier for women to run in Parliamentary systems rather than in a more direct democracy system. With a Parliament system, you can become a great advocate for your party's views, making you as valuable as any other person, with the added benefits of tokenism. When you're running for election among real people, you also have to deal with certain stereotypes. Successful female candidates always seem to behave hyper-masculinely (Clinton, Thatcher, M from Bond) or very nurturing and non-threatening (Palin, Sheila Dixit), but they have the advantage that it's harder to attack them without looking bad. Widespread acceptance of female leaders is going to take a bit.
I suspect that as China goes democratic, it will also follow a one-party democracy. Running political operations in all Chinese states is very expensive, so a single party can take advantage of economies of scale. Meanwhile, there is a relative population homogeneity and relative policy consensus. Most political disagreements center on personality differences between rival power cliques, which currently takes place behind closed doors but could easily be democratically decided. The government is very popular and would easily win elections; popular pressures already determine much of state policy. The big difference might be on foreign policy, in which a democratically elected government would be constrained into acting more hawkish on a world stage to save face domestically. Economic policy would also probably become more distorted through the influence of rent-seeking interest groups. On the plus side, voting out incumbents is a great way to let of political steam. Right now this is taken care of by the occasional execution or firing of the designated fall-guys, but if conditions are bad enough you want the guy at the top to change too.