First a clarification. I wrote 24 volts in a few places. The schematic actually says 25 volts and you might measure even more across the transformer because the wall voltage might be higher today than it was in 1963 when games might have had a low tap option on the transformer because power wasn't as consistent as it is today. None of that really matters because the games probably worked fine in a range of voltages in the mid 20s. So let's just call it full voltage instead of 24 or 25 or whatever.
So in the first case with no special, when you hit any bumper you end up with an interlock relay coil and the P relay coil connected in series across the full voltage. The switches that close to allow current to flow can be thought of as ideal and cause no voltage drop. For practical purposes that's true. So you have two coils, about 3 ohms each wired in series across the full voltage. Since they're wired in series we know the current through the pair is the same, and since their resistance is roughly equal we know that the voltage drop across each coil is about the same too. So each coil sees the current of about 4 amps (or about 24 volts/6 ohms) and a voltage of about 12 volts (since the resistances are the same the voltage across them must be the same).
The P relay coil (A-487), and both types of interlock relay coil (A-6821 and A-7687) are intended to operate in series so they work just fine at half the voltage by design. There are several other games that use coils in series like this, Mibs for example, typically when there are a bunch of targets or rollovers to hit and each one has to add the same number of points. The P relay coil fires any time any of the other targets is hit and is what awards the points as Gigi does. It saves having an extra switch on each target to just add points.
What makes Gigi interesting is that once the special is lit the P relay coil is effectively replaced with the N relay coil which has a much higher resistance as you measured. Ordinarily the N relay coil (A-489) gets the full voltage to itself whenever the P relay switch, or any other 1 point switch closes. There's no difference between the various 1 point switches. There could be a dozen of them but since they're all wired in parallel, any one or more of them closing will connect the N relay coil to the full voltage. So normally the N relay coil draws about 1.5 amps (or about 24 volts/16 ohms) at the full voltage. Again no problems, that's what it was designed for.
However, when the N relay coil fires in series with one of the interlock relay coils things are very different. The current through the two coils is about 1.25 amps (or about 24 volts/19 ohms). The voltages across the two coils are not the same since their resistances are not the same. The N relay will see most of the voltage, about 20 volts (or 16 ohms/19 ohms * 24 volts) while the interlock relay coil will see only about 4 volts (or 3 ohms/19 ohms * 24 volts).
The N relay coil can apparently operate reliably in both cases but the interlock relay coils do not work with just 4 volts and 1.25 amps. So they're deliberately failing to operate to avoid unsetting the special until the ball drains. They do consume power and will get hot if left on, but they just don't get enough power to actually trip the interlock.