Unexpected resistor for oscillator
The answer depends on the kind of inverting amplifier you are using.


case 1: If the active unit has a finite output resistance rout (medium-to-high valued) the additional resistor is indeed not required (however, it may be included - and it influences the time constant for CL2).
case 2: If, however, the inverter is realized with an opamp (low output resistance rout with an unknown value) such a resistor is necessary to determine the associated time constant. Think, for example, of an ideal opamp inverter with zero output resistance - the capacitor CL2 would be useless because it would act simply as a load without any influence on the feedback path.
Additional explanation: The working principle of the oscillator circuit is based on a feedback path consisting of a third-order lowpass. This lowpass contains a first order lowpass section (the first two elements) in series with a second-order L-C lowpass. (The inductance L is realized with the crystal). This 3rd-order lowpass is able to produce the necessary phase shift of -180deg at fixed frequency (as required by the Barkhausen criterion).