Selecting proper resistance based on tolerance
Moved long comment discussion to Answer so I could add pretty pictures.
To answer the original question, you don’t need particularly precise resistors for this circuit. The capacitor is 1% at best, and the current that Vout feeds R1 depends on how close to the rails the Vout opamp can reach, which adds uncertainty to the overall tolerance (1% error if opamp only swings 0.05V to 4.95V). So 1% resistors are just fine.
Here is the original circuit with convenient values, assuming single supply +5V rail and rail-to-rail opamps.
The V0 opamp swings the full 0V to 5V.
The V1 opamp has a gain of 1/5 so swings 1V, centered around 2.5V, so from 2V to 3V, inverted.
The V2 opamp has a gain of 3 so swings 3V, centered around 2.5V, so from 1V to 4V, inverted again.
This V2 voltage feeds the integrator current through the 100K plus resistance under measurement, R.
For R=0, the current through the 100K is (4-2.5)/100K or (1-2.5)/100K, or +/-15uA.
For R=200K, current is (4-2.5)/300K or (1-2.5)/300K, or +/-5uA.

If we instead remove the V2 opamp and drive the integrator straight from V0 then the only change is the driving signal swings 5V instead of 4V.
By changing the fixed resistor to 166K we get the same +/-15uA we had before for R=0.
For R=334K, current is (5-2.5)/(166+334) = 5uA.
So the 4 opamp circuit yields a 5-15uA range for a 0-200K measurement.
The 3 opamp circuit yields the same 5-15uA range for a 0-334K measurement.
C sets the frequency range.

Here is a simulation of the 3 opamp version using rail-to-rail opamps:

EDIT #2:
If you want to achieve exact equivalency to the original 4 opamp circuit, that can be done with one more resistor. The R5/R6 network divides down the Vout signal to exactly what the original V2 output was, and their parallel impedance is chosen to duplicate the 100K Rbias.

OK, so that's how you do it with 3 opamps.
But now I have a question: This circuit is just an RC oscillator. Why on earth would you use 4 or even 3 opamps for such a thing? There is a very common 1 opamp circuit for an RC oscillator, why not use that?
I don't think adding more opamps makes the final measurement any more accurate: you're still limited by the tolerance of the R and C and the opamp's output swing consistency. If there's some reason for all the extra complexity I'd like to hear it.