The Keithley 2510 acts as a really good quality regulator, and this way still shows that thermal setup is capable to get the good stability. However using one the one sensor also used for regulation is kind of cheating - it does not tell very much on how stable the temperature is at other positions in the box. The small box also helps a lot, as this makes it fast (time constant is proportional to the square of the dimensions). A faster system can have more feedback at a given frequency.
If the Ke2510 is using the build in PID function, there are still two points where a special purpose TEC regulator could improve on it: The nonlinear current to power curve is usually relatively well known and the other side temperature can also be compensated.
The critical part for true stability is the sensor and the part to get the temperature reading, not the output part of the controller. So if you want to build a controller it is about the ADC, not so much the PWM (or DAC) resolution. With a suitable sensor, it is not that difficult to get mK resolution for the temperature reading.
The stability does not even look that good - at least with a second sensor a purpose made TEC controller should get better stability.