I suggest a logical link from the WWII low-flying fixed-wing aircraft, through helicopter gunships such as the UH-1 Iroquois with their side-firing machine-guns, then on to late 80s/early 90s helicopter games and assorted shoot-em-ups to FPSs. I assume that for most of this time, the player was firing while moving sideways.
The first step (from fixed-wing to helicopters) seems logical, following the change in which aircraft carried out low-flying ground-attack missions. There are plenty of reports of helicopters strafing targets from around this period, such as
a dozen u.s. army and marine helicopters strafed the landing zone
Xin hua tong xun she 16 Mar 1965 (News from Hsinhua News Agency: daily bulletin)
It's certainly clear from some of these sources that forward-firing guns (and for that matter fixed-wing aircraft) were used, but this (more modern) picture of the side armament of a UH-1 gunship clearly shows the door-gunner's machine-gun:
Crucially such guns would be fired while the gunner was moving sideways (as he faced out the door -- this traversing fire seems key.
The next step is into gaming -- in the late 80s and early 90s there were many helicopter flight-sims, though of course they're from the pilot's viewpoint. This was also the era of vertical- and side- scrollers, and I recall side-firing guns being a power-up in some such games (such as the space-themed Hellfire)
In general strafing by moving sideways while firing was commonplace in scrolling shoot-em-ups, thus predating the FPS use in Wolfenstein by a few years.
Google books provides tantalising hints from this period:
Both Zaxxon from Datasoft and Blue Max from Synapse are three-dimensional flying shoot-em-up games with landscapes that scroll one pixel at a time. In each case ... In both games you have to strafe the enemy on the ground, and fight enemy planes in the air. Zaxxon is ...
Practical Computing - Volume 7 (1987) Page 134 (unfortunately the preview is minimal and misses that text)
A link to helicopters in games comes from this reference to Thunder Blade (a rail shooter from 1987) in which weapons fire forwards but the helicopter can move side to side as it follows a pre-determined path
but the reward comes in the form of a
nice easy strafing job on what looks like a large
ACE Issues Oct 1987-April 1992