According to Wikipedia:
Kotok-McCarthy also known as A Chess Playing Program for the IBM 7090 Computer was the first computer program to play chess convincingly. It is also remembered because it played in and lost the first chess match between two computer programs.
Leaving aside the inconsistency between being "the first computer program to play chess convincingly" and losing the first computer match, it looks like this match was the first.
The article continues:
In 1965, McCarthy, by then at Stanford University, visited the Soviet Union. A group using the M-2 computer at Alexander Kronrod’s laboratory at the Moscow Institute for Theoretical and Experimental Physics (ITEP) challenged him to a match. Kronrod considered Kotok-McCarthy to be the best program in the United States at the time.
...
Georgy Adelson-Velsky, Vladimir Arlazarov, Bitman, Anatoly Uskov and Alexander Zhivotovsky won the correspondence match played by telegraph over nine months in 1966-1967. The Kotok-McCarthy program lost the match by a score of three to one
So, it looks like the very first engine vs engine game was played in 1966. The game given in the question was the third of four and the US computer engine, Kotok-McCarthy, drew two and lost two.