For many of these aircraft weight considerations were an issue (engines were weaker and subsystems were heavier back then). My guess is that they couldn't install a hydraulic pump big enough to retract both wheels simultaneously and that's why they retract in sequence, not enough hydraulic pressure.
By the way this happens in many aircraft, not just the 111, plus it's easy to observe in wartime films that this behavior was fairly common for a lot of types.
That being said, i don't know if it applies to restored warbirds at airshows since many of them now have upgraded internal systems to conform with civil aviation standards, so watching a clip from a present day airshow might not exhibit the same traits. Hope it helps
