Working of INA826 instrumentation amplifier for Pt100 RTD
Is this circuit amplifying only the voltage across the RTD or are any
other voltages involved?

It's amplifying the voltage across the RTD. The 10k resistors in conjunction with the 100nF caps have a filter time constant of 1ms.

Why not connect -IN to GND, and +IN to a junction of a 5V voltage
divider consisting of known resistance and the RTD?

The common mode of the instrumentation amplifier would not support low voltages when at 5V as shown in the graphs below (at a gain of 10 the common mode would be between the blue squares as only gains of 1 and 100 are shown). If the output of the amplifier were at 5V then the input needs to be centered around 2.5V or the instrumentation amplifier would not gain up the signal correctly.


What is the advantage of the present schematic over the one mentioned
above?

The ability to amplify all of the RTD's resistance range.