Have you done any volume adjustments?
Yes, and that caused it.
Just like in AHII, I had turned down the Master Volume to about 20% (no adjustment to any individual sound groups). This did cut out the engine sounds only, and only on all bombers. Playing with that master slider I find a very sudden engine sound cutoff at/near approximately 25% of volume, it goes from still quite loud (ony my system) to none.
With all fighters I tested, the engine sound volume scales much better across the whole range when using the master volume slider.
By the way, when I tried to check this, I could not start DX11 nor DX 9 version of AHIII. The splash screen came up, but never the clipboard. Was able to close the window without problems (no "has stopped responding" or so). I had previously played AH II and did exit that one regularly.
A reboot fixed this problem-