Windings 1-3 and 2-4 are the same. The rest are "12V" windings.
If you connect the 1-3 and 2-4 in series the turns ratio will change from 2.5:1 to 5:1 and the output voltage will go down by half.
You should be able to put the secondary winding in parallel or in series depending on what you want.
The odd (to us, natch) setup is due to the use of standard parts, and linear regulators.
Assuming the STANCOR P-8667 (28V, 1A) and P-8380 (10V, 3A) were standard off the shelf (read: cheap and easily available) transformers, since Steve and Steve were building this, from scratch, in their garage, having sold their car for funding, and expecting to sell it as a partial kit. The customer would have to provide the transformers.
Then we figure out the best arrangement to maximize efficiency while minimizing heat. They only had linear regulators at the time, not very efficient, high drop out voltage, physically big. Not like today's high efficiency tiny switching regulators with millivolt drop outs. The LM323 for the +5V rail is a 3 Amp regulator. Assuming all 3 Amps were needed, that means 30 Watts through that lone Transformer, half of which is wasted on the Regulator. 15 Watts of heat right there. Same for the 12V reg, at 1 Amp, that's 28 Watts through the regulator, 16 Watts wasted.
Had they connected the 5V regulator through the 12V regulator, they would 1, need a much beefier 12V regulator, as well as a much beefier transformer. Combined they would need to carry at least 28V * 4A = 112 Watts, for the combined +12V (1 Amp) and +5V (3 Amp) draw. 64 Watts of which would be wasted on the +12V regulator as heat, and another 21 Watts wasted on the 5V regulator.
Comparing the two numbers, we get a waste of 31 Watts in the chosen design, and 85 Watts in the Single Transformer, Series Regulator design. Did not account for any loses from the rectifier or transformers, minor in comparison.
Consider the cost of electricity, heat management, and the planned need for customers to source their own transformers, which two smaller ones would likely be easier to find than one beefy one, the design is the smart choice.
If you read anything about the construction of the Apple I, keep in mind, that it revolved around two cash strapped guys working out of a garage. Cost was always a concern. The thing didn't even use ram for the display, they used shift registers cause it was cheaper.
Best Answer
One interpretation is that rating is not there to give you any indication of how the transformer should be used in a flyback application, but only to tell you what peak voltages it was designed to work with. The likely reason for this is there are too may conditions, caveats, and gotchas with different flyback applications to give you a simple number rating. But a maximum working voltage is easier to give.
Since you don't use a transformer by running DC through it (which is what a DC rating would imply), you would have to use sinusoidal AC voltage to obtain this maximum working voltage. Square waves and pulses, which is what you actually use with a flyback transformer, are not true DC.
You get something similar with ferrite beads where the current rating tells you when the ferrite bead will over heat, but you never use it at that since the ferrite bead saturates at much, much, much lower currents defeating the purpose of the bead if you use it anywhere near the current rating. But it's an simpler number to give.