According to the authors of the article, they don't violate any physical or philosophical principles. To explain this further, let's think about the role that time plays. An object, seen any instant, is a three-dimensional cross section of this worm. At any point, the angle your worldline makes with the time axis is a measure of your speed. Relativity requires that worldlines be timelike.
Massive objects distort space-time and bend worldlines.
Suppose space-time becomes so distorted so that some worldlines form closed loops. Such worldlines would be timelike all around. Locally, they would have all the properties of space and time, but yet they would be corridors of the past. By following a CTC, we could meet ourselves in the past, or if the loop were large enough, visit our ancestors. CTCs can be created by distorting space time.