Hello Leenchen64
Provided you have a national point-to-point group ticket from Zürich Airport to Neuchâtel, you can in fact take any train. It is OK for a ride to Zurich HB (not Hbf, that is used in Germany and Austria only, here it’s just HB).
However, the railways do reserve seats for you on the trains as confirmed on your itinerary. You can use other trains provided there is space left, but this is not the idea behind a group ticket. With a group ticket you get a discount, on the other hand, since you announce your trip at least two days out, you allow the railways to plan their rolling stock ahead of time, to assure there are enough seats for all the groups and individual travellers. This is not possible if you just take any train.
Kind regards,
Roland