That's highly speculative and glosses over a lot of the details. The idea that it can be done with today's tech for "reasonable amounts of money" is laughable. The launch costs alone for putting 500,000 tons into orbit already kill that idea.
For a point of reference, SpaceX currently charges about $2,720/kg for LEO. So to get this project off of the ground (literally) you're talking about $1,360,000,000,000. And that's just launch costs. It doesn't include the invention of spacecraft that can survive in deep space indefinitely without resupply, the materials science advances needed to survive 300,000 nuclear explosions (the paper suggests 1mm of stainless steel coated with a thin layer of oil), or the fact that this is only talking about getting to a place we probably don't even want to go.
And this is kind of the point. Once you've invented all of the necessary pre-reqs there's really no point in hitting it with 300,000 nuclear explosions, you already have a self sustaining space colony. You can continue to build those pretty much forever and never ever come close to running out of room. There's no need to travel to some other star system at that point. The sense of adventure has to be weighed against the risk factor of detonating 300,000 nuclear bombs without incident and all of the yet unknown hazards of interstellar travel. Oh, and thanks to the tyranny of the rocket equation it is a one way trip unless you're packing a nuclear bomb factory and enough mining equipment to get the raw materials you need from whatever you happen to find at your destination.