Leave it to Yale to come up with it! This isn't a PhD program, as the almost complete lack of required coursework, makes clear. Indeed, the core bit of required coursework--"a two-semester pro-seminar on canonical legal scholarship and methodologies"--is just a variation on a course that a number of law schools (including my own) already offer to J.D. students. So what this new program will really be is some combination of resume polishing and an opportunity for people interested in law teaching to have an opportunity to write--in the latter regard, it will be a somewhat longer Fellowship than the two-year ones which are now quite common. A Ph.D. it won't be, however, and it's inconceivable, given the lack of an actual Wissenschaft the program is meant to instill, that it will confer the advantages that JD/PhDs in cognate subjects have as scholars and on the teaching market. But as a three-year writing Fellowship, fully funded by Yale at this point, it will no doubt be attractive for those who want to go into law teaching but don't want to earn a real PhD.
UPDATE: More thoughts here.