This was the second of two matches played between these two players within a year, and was played between December 1862 and January 1863.
Mackenzie had lost the first match in the summer of 1862. The exact score of that match is not clear. The Illustrated London News quotes a letter from MacDonnell giving his combined result against Mackenzie (after the second match) as +10-10=4 in which case Mackenzie's score for the first match was +4-7=3.
Mackenzie gained his revenge defeating MacDonnell by +6-3=1. The Illustrated London News of 20 Dec. 1862 (p. 654) states this match took place at the Grand Cigar Divan in London (now know as Simpson's in the Strand).
When this match was played, it represented a very high level encounter indeed. The players were of similar strength and in their prime, Mackenzie being 25 years old and his opponent 32. They were both in a group of elite players who strength at the time was just under that of the leading masters: Paulsen, Anderssen, Kolisch, Steinitz. Chessmetrics has MacDonnell as 6th and Mackenzie as 13th in the world at the time.
Mackenzie's rated strength, however, was to increase significantly with regular tournament practice as a professional player in the USA, whilst MacDonnell, who was a priest, did not match his erstwhile opponent's improvement.
This was a strongly fought match, and featured interesting new ideas. MacDonnell's defence in game 8 and 10 prefigured Chigorin and the Hyper-Moderns.
Progress of the match:
MacDonnell led 3-2 after 5 games but then could make only one draw in the remainder of the match. Of the two players, he made the most egregious blunders, but also played the more inventively in defence.
Mackenzie : 0 1 1 0 0 1 1 1 1/2 1 = 6.5
MacDonnell: 1 0 0 1 1 0 0 0 1/2 0 = 3.5
The chronology of the match as given in "The Era" is:
14 December 1862: MacDonnell 1, Mackenzie 1, draws 0
21 December 1862: MacDonnell 3, Mackenzie 3, draws 0
04 January 1863: MacDonnell 3, Mackenzie 5, draws 1.