It is an interesing story. I assume that it is believed that "mille kine" refers to a thousand cattle.
Mille is the celtic word for thousand, but kine does not seem to celtic at all. It only appears as an english word. I would find it hard to believe that the name is derived in this way.

Mulligan is derived from the Gaelic surname O'Maolagain. It is my understanding that Milligan, Milliken, Mullican, Millikan, Mullican etc. are also derived from this surname. The spelling discrepencies come about from several factors including illiteracy, poltical differences, religious differences, Ellis Island etc. Perhaps there is someone out there that can shed more light on some of this. Dan