I'm not sure how helpful it's going to be to simply look at the extension itself. It was built quickly and the code is probably not as tight and easy to navigate as it should be since it ended up being touched by a lot of different people. The basic idea is that you first send a POST AJAX call to the BigQuery API which queries the data set. In this demos case it's something like this:
SELECT mother_race, mother_married, COUNT(*) as count FROM [publicdata:samples.natality] WHERE (mother_race in (0, 1, 2, 3, 4, 5, 6, 7, 9, 18, 28, 38, 48, 58, 68, 78)) GROUP BY mother_race, mother_married ORDER BY mother_race;
These numbers and what they mean and why we had to use them gets extremely convoluted and isn't really important, but it was the nature of the data. But in general, this is a pretty standard syntax for querying data. Then, the code waits about a second or so while BigQuery gets the results, then sends a GET AJAX call to retrieve the results. The data comes back in JSON notation, and the extension then parses through all of the code.
So the part that shows the bar chart is not as important to the demo since it's just using a 3rd parting JS visualization library to display the data. You could use anything you want to display the data in the extension. The important piece is that it's going out to BigQuery and retrieving results based on a huge data set and bringing it into the extension. Beyond that it's just like creating any other extension.
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