Op-amp input resistor?

 I answered this SE EE question a week ago.

My answer

My motivation

This is really a very old question and should be of no interest to either the OP or the "reputation accumulators" here. But my hope is that there are still inquisitive people here who will appreciate revealing the basic ideas behind these famous circuit solutions…

What is it?

This is not a "true instrumentation amplifier" but simply a "differential follower with buffered inputs". The difference between the two circuit solutions becomes quite significant when the circuit is required to amplify.

In this "fake" instrumentation amplifier, the input stage passes (does not amplify) both common-mode and differential signals. If you try to make it amplify (simply making the followers non-inverting amplifiers), it will amplify both common-mode and differential signals because the non-inverting amplifiers are separated. Therefore amplification can only be done with the second stage, which has some disadvantages.

In a "true" instrumentation amplifier, the input stage passes the input common-mode signal without amplification, and amplifies only the differential signal (in addition, the second stage may also amplify). This is made by a clever trick - connecting the bottom parts (resistors) of the input non-inverting amplifiers by a common resistor Rgain. As a result, the non-inverting amplifiers interact to each other and a virtual ground appears at the midpoint inside Rgain in differential mode.

Why then...?

The obvious question arises, "Why then is the better circuit not shown in the data sheet?" I think the answer is simple - this (circuit solution) was not the manufacturer's intention but rather to illustrate in some way some application of its quad op-amp…

See also

See more about the philosophy behind the ingenious "true" circuit solution in my Codidact paper What is the idea behind the op-amp instrumentation amplifier? There I have tried to show the reasons that led to the evolution of this "fake" instrumentation amplifier into a true one.

See also my recent answers in:
Understanding Rgain of an instrumental amplifier
Why use a three op-amp instrumentation amplifier?