I think you are missing the point.
First, the article doesn't care what you want.
Second, it is using the current population density of Brooklyn, and that is with the current transportation infrastructure. If your foreseeable maximum travel distance was 100 miles, none of this would be necessary. It is very unlikely you or 99% of the people would need cars. Transportation would be optimized for mass transit/walking/biking. It would probably feel less crowded than current day brooklyn.
I think you'd need something of a revolution in transport infrastructure to serve a Brooklyn that was the size of New Hampshire. With the current Brooklyn, the longest public-transit trips, if you're very unlucky with where you're going to/from, are about 90 minutes, and most are around 30 mins. But if you just organically grew out the same infrastructure to a Brooklyn the size of New Hampshire, it would take 5+ hours to get from one side of New Brooklyn to another.
But why would you _need_ to get from one side of New Brooklyn to the other any more frequently than you need to get from one side of the US to the other today?
Business travel (ie, flights, currently). Less than shipping, but still frequent.
Vacation travel. More frequent than business, but likely shorter distances (still often above 100 miles, though). Though I know of over a dozen people in my circle of friends who have travelled over 1000 miles to get to their spring / summer locations. And these are relatively poor college students.
The problem isn't based around an expected increase in frequency (though there would be, as things are closer), it's that a large number of people do need such large-scale transports, and shoving more of everything together brings up new problems (look at Chicago, the roads & tracks are fairly nightmarish in many places).
It would require a massive infrastructure project to build up an area that big and dense, so let's assume transportation is part of the plan. A mesh of rail lines could be put in with high speed rail with a few stops at the coarsest level of the grid, moderate speed rail with more stops in the middle, and the equivalent of the NYC subway system at the finest level of the grid. The system could be planned out so that no two points are more than a few train changes and an hour or two apart. That's much better than our current national transportation system.
Shipping could have a parallel system at the high speed and moderate speed, using shipping containers and (while we're at it) automated transfer systems for the containers. Maybe the whole place could be rigged up like a giant FedEx shipping center, with hundred-mile-long conveyor belts.
Second, it is using the current population density of Brooklyn, and that is with the current transportation infrastructure. If your foreseeable maximum travel distance was 100 miles, none of this would be necessary. It is very unlikely you or 99% of the people would need cars. Transportation would be optimized for mass transit/walking/biking. It would probably feel less crowded than current day brooklyn.