Though the uploader attributes this to Kirnberger, there is no source for that. Further, Kirnberger's Wikipedia page says he was a composer "primarily of fugues". This march exists in Elias Howe's Musician's Companion (see below), but probably arranged by him, not composed by him.
Published in The Musician's Companion (Howe, Elias) (Boston: Charles H. Keith, 1843), part 2 p.24. It is not known if that is the first publication. This collection was compiled by Howe, but only about a quarter of them are original, so this is more than likely arranged. No composer listed. Anonymous for now, but subject to correction, as is instrumentation, if a composer is definitively found, and if an earlier original instrumentation is found.
According to The Fiddler's Companion, "GOVERNOR KING'S MARCH. American, March (4/4 time). USA, southwestern Pennsylvania. D Major. Standard tuning. AB. An old fifer's tune. See note (Bayard, 1944) for "Old Man and Old Woman Scoldin'". Source for notated version: Hiram Horner (fifer from Westmoreland and Fayette Counties, Pa., 1944) [Bayard]. Bayard (Dance to the Fiddle), 1981; No. 153, pgs. 88‑89. Howe (Diamond School For the Violin), 1861; pg. 24."
Despite apparently being from Pennsylvania, there were no Pennsylvanian governors named "King" in the 19th century, so it is unknown who this was written for/about.