It is in part a survey artifact. I can tell you that the boundary is the position of the very short 1881 Cimarron Meridian and related baseline for the rural survey grid. The story of that meridian is that it was meant to serve as a survey base for a "no-man's land" that fell between the definition of several territories after Texas took its boundary south so as to avoid crossing the "slave state line" in 1846. So it's a leftover bit, not surveyed because it was unincorporated "Indian Territory" and so theoretically didn't need it until land pressure forced the issue in the late 1870s. But as to why it's not in line with New Mexico's boundary? That's a simple human surveying error, but because the Cimarron Meridian legally defined the boundary of this no-man's land, New Mexico got to keep that two miles to the west. The ranching and other rural leasehold interests in the region would have taken a rather dim view of the Federal Government slicing that two-mile strip back off, so I suspect it wasn't worth the legal trouble of correction then and hasn't been since.

Bill Hubbard's American Boundaries (Chicago: Univ of Chicago Press, 2009) may talk about this in chapter 9, but the book is not here with me right now.

TL,DR: A surveyor, a theodolite, and some bad math.