A concise explanation of "of that Ilk" may be found in MacKinnon of Dunakin's brief book, Scotland's Heraldry. All of this silliness about this style is starting to get to me!

To wit:
"In the Lowlands...the expression "of that Ilk" was used to designate the laird who held the place from which the family took its name, and who was head of the whole name. The word "ilk" simply means "same" and, in charter-Latin, Dundas of that Ilk was called "Dundas de eodem." Thus Dundas of that Ilk was head of the whole name, and Dundas of Duddingston was head of a cadet family whose seat was Duddingston.
Some of the Highland chiefs, to make their status clear at Court and when travelling outside of the Highlands, adopted the style "of that Ilk," early examples being MacLeod whose arms are given in Workman's MS, circa 1565-66, as MAK CLOYD OF Yt ILK (i.e. Dunvegan), and MacLachlan was styled "of that Ilk" in 1573. The use of his territorial designation might have made a chief appear, to a Lowlander, as a mere cadet. ...
About the beginning of the 19th century, many of the chiefs, especially those from the Highlands, because of the difficulty of explaining "of that Ilk" when they visited England, adopted the well-known style of duplication of the patronymic; thus MacGregor of MacGregor, MacKinnon of MacKinnon, MacLeod of MacLeod, and so on. In some cases both the double patronymic and the territorial title is used, as in MacDougall of MacDougall and Dunollie, MacMillan of MacMillan and Knapp, and so on, and this is particularly the case where the clan lands remain in the possession of, or have been recovered by the chief."