If my understanding is correct, the explanation you found means "The finish is called kyokko and, as the name suggestions, has a radial pattern reminiscent of the sun's rays."
The equivalent in English is the "Soleil" finish which has a similar meaning to the Japanese: "As the name suggests, the finish resembles the sun’s rays. It consists of a very light satin finish that originates in one point and spreads in a radial pattern on the rest of the surface on which this finish is made." (First reference link, No. 5).
From the context and my research, 目付け seems to mean something like "appearance". According to some online dictionaries (such as the one in the second reference link), it's used in kendo to mean "to look at an opponent in their entirety", so it possibly means something like "the appearance (of the watch face in its entirety)".