Fans that look like this:
Is it to somehow help the balance of the engine?
It isn't something restricted to old vehicles; my Lumina has fans like this, though not as irregular as the picture shown in the question.
As far as I can recall, the chief reason cited for this by the manufacturer is noise reduction. You'll notice the additional weight on some of the blades to ensure that rotational balance is maintained despite the asymmetry.
The oddity is there to lessen fan noise. The uneven spaces creates air pulses that cancels out some of the noise, without lessening the ability of the fan to move air.
It may be to allow a hand/tool to access a screw or bolt that would otherwise be inaccessible if there wasn't one opening between the fan blades large enough. Although I can't think of how that would apply to electric fans