Is this a documentation error?

Either this was a transition product to the 3V PS/2 or someone replaced the 5V board with a 3V board.  The user's manual clearly shows a 5V board, but that's not always correct.

In either case, you got a better product, the 3V board is much more desirable.

I guess I've always been a little confused about that.  Does the 5V board correspond to the 9V battery?

Isn't this the 9V battery at the end of the red arrow?

Yes, if you have the 9v battery (8.4v 7-cell rechargeable), then you have a 5V board.  If you have the 2-cell 2.4V battery, then you have the 3V board.  Another easy way to tell is the charging port for the 5V board is round and the charging port for the 3V board is rectangular with a couple of bobbed corners.

That was a 2004 product and should be 3V.  MTh would cut and paste instructions to make a new one.  So maybe in transition it was missed.

5V versus 3V has to do with processor operating voltage not battery voltage.  A misnomer anyway as there is a 5V power supply on the PS-2 3V too.  It powers the 3.3V power supply for the processor.   The new PS-3 boards have about 5 power supplies of various voltages.

PS-2 5V uses 8.4V battery just like PS-1.  PS-2 3V uses 2.4V battery.   PS-3 uses supercaps that operate at 5.0V.  PS-2 3V supper caps also work at 5.0V.  Each cap is rated at 2.7V.  2 in series.  The charging sources for PS-2 3V and PS-3 is 5V power supply so they charge to 5V.  G