putting aside the mis-information. the higher the voltage the more the heat and the greater the wasted energy. and yes, if you tried to run at 12 volts, the wasted heat would burn up that battery in short order.
try running the motor on 5 volts. low heat, good movement, no problems.
not sure how to emphasis APPLICATION.
if I were to ask how to size a resistor for an LED that needs 10ma and I wanted to use a 100 volt power supply because that spec sheet says I was allowed to do, because the resistors are good up to 100 volts, I would have the whole community down on my head.
your application does not require anywhere near an amp nor anything over the nameplate voltage of the motor. in fact, you probably could get away with using 1.5 volts to drive the motors properly. that is once you allow for the driver inefficiencies.
what others are missing is that your APPLICATION requires a PROPER driver. like a simple H-Bridge.
of the required type; suitable or appropriate.
the key word here is appropriate.
if you were making the whole chess board get up and walk around you might need that 9 volts. if you wanted to do it fast, you would way over volt the motor and pump in 12 volts, but that would not be proper for this application. Then you would be discing the need for a fan to blow away all the heat energy created by the wasted use of too high of a power supply.
You are only moving arms that move a magnet. and even doing that slowly. I cannot imagine trying to run a chess piece at 600 inches per minute only because you have a 12 volt power supply and could not figure on how to get the proper voltage.
and I cannot imagine using a micro stepper to move a chess piece. well, how many zeros of positioning accuracy do you need ? if you feel the need to get past 3 decimal places, then a micro-stepper could help.
Since you can drive any stepper (in the hobby range) on 1.5 volt batteries, you can try it out for yourself on your bench.
set up a bunch of switches to simulate an h-bridge, connect a simple D cell and then push the switches in sequence. just remember coil 1 then coil 2 then coil1-reverse, then coil2 reverse and repeat.
don't fall for the 'high voltage' power that people unfamiliar with the proper application of steppers seem to recommend as a starting point without understand the proper application of steppers, drivers or power supplies.
the ONLY reason you EVER need too increase voltage is to increase power.
power is based on the APPLICATION.
power increases proportionally with voltage.
iron loses, that is heating, increases with the square.
the APPLICATION requires 1.5 volts. maybe 3. EVERYTHING else is wasted as heat, both in the chip and the motor.
what is the real pity is that to compensate for poor engineering is the selecton of circuits that allows for the poor selections of power and fool one into thinking they did something right.
I have to say that it is getting tiresome to keep seeing people give incorrect advise.
// rant mode off, just