Vidhatri is built out of the same root as Dhatri, and the difference between the two names is a prefix. The root dha means to put, place, set or found, and it is one of the busiest in Sanskrit. Dhatri is its agent noun, the one who places. Add vi, which distributes, disperses or sets apart what the simple root establishes, and the result is Vidhatri, the one who arranges, allots or disposes. Where Dhatri sets a thing up, Vidhatri decides how it falls out.
That is close to the whole of him. He has no story, no attribute and no iconographic type, and outside the pairing he barely occurs. In classical Sanskrit the two names travel together as a formula for the ordering power behind events, and a reader meeting Vidhatri usually meets Dhatri in the same clause. It is a genuine feature of the later Vedic period rather than an accident: abstract functional names were being promoted into gods at that time, and Prajapati, the lord of creatures, and Vishvakarman, the all maker, came up by the same route and at roughly the same moment.
The pairing outlived its own theology. In later devotional and vernacular usage the disposer becomes a way of speaking about fate, the power that writes what will happen to a person, and Vidhatri under the form Vidhata acquires a life in popular religious speech out of all proportion to his textual footprint. How and when that happened, and by what route a formula for divine arrangement became a name for personified destiny, is not something the surviving Sanskrit sources set out. The atlas records the gap rather than filling it, and the entry carries an open question naming the work that would close it.