Hi there,
Yes the circuit is not drawn correctly, nor is it designed correctly.
I've included a drawing of a circuit that would work as desired given the thermistor resistance data posted in the first post of this thread. Note that this kind of circuit requires a thermally stable positive voltage reference (the +7v supply) and if it is not stable then a voltage reference diode should be incorporated into the design rather than using the power supply as a reference.
I've also included a plot of thermistor resistance vs output voltage, and linearity data.
You'll note a few changes that were not in the original schematic which i will list here for reference:
1. The inputs to the op amp are swapped. This is necessary.
2. The positive voltage to the LM324 power supply terminal is +7v not +6v as the original schematic had. This is because the LM324 can not reach as high as 5.00v output with only a 6.00v power supply. If a 7v power supply is not available then i would suggest either using a rail to rail op amp instead of the LM324 or else relaxing the requirement of having to get the output all the way up to 5v (maybe 4.4v would be ok).
3. There has been an additional resistor added to get a zero volt reading for the desired thermistor resistance.
4. The thermistor was swapped with the original 1k input resistor. This is necessary to get the right slope of the output voltage vs thermistor resistance.
5. The op amp resistors were changed, one 10k went to 100k and the other 10k went to 120k. This is necessary to get the right scaling.
6. The negative 10.5v power supply was connected to the negative power supply terminal of the op amp. This allows getting the output all the way down to zero volts without any issues. If this is not possible in the real life application, you may have to go to a rail to rail op amp or else relax the requirement that the output has to get all the way down to 0.000 volts (0.050 volts might be possible).
7. You'll want to note that the output voltage vs thermistor resistance is not a perfectly straight line, although it's not too bad. To improve the linearity raise the lower 1k resistor and adjust R4 at 25 degrees C temperature for 0v out and adjust R3 at max temperature for 5v out. For example with R1 raised to 2k, R4 changes to 100.5k and R3 changes to 163k (approximately). I've included a comparison of R1 vs the linearity in the second attachment, but the x axis is really a percentage of the thermistor resistance normalized to 1k, so at x=1 the thermistor resistance is 1k and at x=0.1 the thermistor resistance is 100 ohms.