What is the incentive structure that facilitates pegging DAI to the dollar?

Very complex. https://github.com/makerdao/dss/wiki

The summary appears to be that participants can stake their non-DAI crypto assets into the system, and then borrow an equivalent amount of DAI at current prices minus a haircut (e.g. 80% of what they put in). This is the way DAI is created. Borrowers pay interest on their borrowed DAI. (How does this not result in a negative total amount of DAI? not sure)

If your borrowed DAI falls below another threshold (e.g. 90%) of the value of your collateral, you lose all your collateral. Someone somewhere gets to buy your collateral for only 90% of its dollar value in DAI, and is incentivized to do so because they can then get 100% of the value back on the open market. Therefore borrowers are incentivized to keep their borrowing below this threshold.

That's a pretty standard DeFi loan system; it seems there are also a lot more tacked-on bits which, I assume, prevent it from melting down in a similar way to all the other DeFi loan systems...