This is simply a fancily designed chain of cities based on the about 40 years old idea of the "compact city". The idea is to reduce urban sprawl, reduce traffic and improve living conditions.
Each link of the chain in itself will be not self-sufficient, but provide all necessary (daily) needs to its inhabitants, including doctors and if not a hospital, then at least competent first aid. No need to drive 20 km for shopping, no need to commute an hour to work and back, your children may walk to their school. Specialised services/places can be reached via public traffic connecting the cities along "the line". Delivery of goods, emergency response etc. all happen via the tunnels connecting the cities.
Still, the marketing says "no streets - no cars" - which is hard to believe nowadays and triggers some sentiment like Tim showed. While this may be the ultimate goal, I think there still will be areas for the lone car to roll around (ambulance, police, milk delivery guy, whatever...) but they wont be comparable to our current road system. Simply an open space without privately owned cars, only a few cars/trucks on official business going about.
So yes, the idea in itself is feasible, yet futuristic, once you look past marketing bling-bling and sentiment.
When it comes to sustainability, it strongly depends on how you build this city, what ressources you use and how you acquired them. Concrete is a climate killer, unless you manage to produce it using renewable energies. Steel is very similar. You can build small villages from local ressources, but a whole city, let alone a chain of cities - that's hard to imagine. This (german) study on the emission of GHG due to subway-construction estimates that one 1 km of subway tunnel "costs" about 100,000 tons of CO2-equivalents. Now you'll have probably two tunnels, both running 170 km under the cities, that's 340 million tons of CO2-equivalents only for construction of transportation infrastructure. Without more detailled numbers on the project it's hard to do estimations - but I think we can assume, that the construction wont really be sustainable, while living in these cities might as well be.