The transformer in this adapter (as in the other HP calculator chargers) has deliberately poor regulation, and appears to the load as having a relatively high (about 10 ohms from what I remember) internal resistance. It may well give 12V+ off-load (or with just a DVM connected), but this will drop when you connect it to a battery pack. A few years ago I connected various load resistors to each type of charger, measured the voltage and plotted the V-I curve. They were all very linear. I still have the data and the calculated values of the open-circuit voltage and internal resistance for various chargers. Let me know if you want this.
I do remember that the zener diodes in this, and in other HP chargers, were a much higher voltage than the transformer would ever give. I remember taking a spare charger lead and connecting it to my bench PSU (0-30V adjustable) with a resistor in series and measuring the zener voltage. I think it was about 27V. The zener therefore has no effect in normal operation, it is there to suppress high voltage transients only.
Finally, the Portable Plus was an HP Laptop computer, an enhanced HP110 (which was called the 'Portable'). It runs MS-DOS from ROM, but is not IBM compatible (neither at the hardware or BIOS level from what I remember). I have a couple, I also have the service manual and technical reference manual for it. It runs off an internal 6V lead-acid battery, but the plug-in charger is the same as the one for the HP41 (and topcats, HPIL peripherals, etc). The techref for that machine certainly mentions the zeners.