Is star grounding sources necessary for this data acquisition system?
First off, system designs like this are an art not a science. It is an art because there are many parameters of the system design that are unknowable (or we don't have time to find them). One could go through the whole system and model it as a giant circuit. To do so one would have to measure/estimate the cables and the noise sources (RFI and conducted emissions through mains AC) takes more time than using best practices.

Short answer:


  Basically what I'm asking is the star connected node(red question
  mark) need to be earth grounded as well?


No, a star ground is only going to add more ground loops and more noise, since you are likely in a good configuration already as per this comment:


  In Figure 2 if I use AI SENSE and if I also route PSU ground to AIGND
  or to the nearest earth I get very good results. So it seems to me if
  I use AI SENSE scheme and a third wire from the red point(the PSU
  ground) to the nearest earth(yellow) or to AIGND(green) things are
  fine.


The idea is to do what works for the noise levels the system needs to attain. If you build the system, and the noise is acceptable for the measurements that need to be made, then your done! Figure 1 would be preferable to figure 2, remember the figures in the NI document are best practices. The environment or setup that you have might not have as much noise, really you would need to have a diagram of the power supply, how its connected to each transducer and a knowledge of the grounding of the DAQ.

Noise and Ground Loops

If the system does have too much noise, then take steps to eliminate it. 
I'll layout some of the best practices in the event that you do experience noise:

The first concept to understand is that of a ground loop. The ground loop starts because there are two points of grounding with two cables. This forms a large loop, if magnetic fields run through the loop (from motors and power lines) it creates a current that runs around the edge of the loop. This creates a problem even with shielded cables via inductive coupling (shielded cables only protect against capacitvely coupled electric fields and block them, but not magnetic), in which a current on the outside of the cable also causes a current on the inside. In most cases it is best to avoid ground loops. 

With a DAQ this creates problems because you might not have total control of the grounding of the sensor wires or the shield. 

If ground loop currents are the biggest source of noise (which depends on the electric\magnetic environment that the system is in) then the best thing to do is break the loop. This can be done by removing one ground (best practice) or by disconnecting the shield (preferably next to the sensor.

Another thing that can be done is to add isolation to the analog signals to break a ground loop, this can be more expensive, but is better.


Source: http://www.sensorland.com/HowPics/IPC07-004.gif
Or this page

It is also good to use twisted pair wire to eliminate loops and keep noise down (this is why most differential signals like RS485 or ethernet have twisted pair. 

Good practices

If you ever build one of these systems again, it would be more convenient from a noise perspective to put the power supplies in the same location as the DAQ. Having a ground on one end is usually the best condition, sometimes the cable can turn into a radiator (antenna), in that case a ferrite can block high frequency signals on the cable. It would also be good to provide shielding around the sensor/source/amp on the end of the cable and tie it to the shield (if the shielding is not grounded, if it is you can break the shield.) 



Watch grounding on both ends as this generates currents if you can help it. 



It's not a good idea to put a power supply on the opposite end unless its isolated.