First, dikes tend to be earthworks, not concrete. Second, the forecast for 100-300 year is 5, not 35 feet. The Dutch were building 5 foot dikes 1000 years ago.
To protect a built-up area like NYC and Long Island, you'd probably build a chain of artificial barrier islands some ways out to sea. That's a simple and comparably cheap earth moving operation.
With current insufficient political will to stop global warming, both the Greenland ice sheet and the Antarctic ice sheet will melt. When Greenland goes, sea levels will rise 20 feet globally. When Antarctica goes, sea levels will rise 200 feet. We need more than an adaptation strategy. We need to curb emissions. Additionally, we will face massive species extinctions, increased ocean acidification, food disruptions and stress on water supplies. Earth moving isn't going to cut it, with all due respect. A focus on adaptation ignores the magnitude of the problem, which in the long term is beyond the power of short-term adaptation to mitigate.
So you're suggesting that The New York Times, hardly a climate-change-denier, got the numbers on their already quite alarmist page wrong by an order of magnitude? I'm pretty sure none of the worst case IPCC scenarios consider the total melting of the Greenland and Antarctic ice sheets.
To protect a built-up area like NYC and Long Island, you'd probably build a chain of artificial barrier islands some ways out to sea. That's a simple and comparably cheap earth moving operation.