I'm part of a TARPN and the main thing we do is chat. There is a simple chat program that runs on the network so we can do realtime multi-user chat. It's pretty fun.
I'm so glad someone who is actually a TARPN user posted here. I am interested in the concept but am far from being able to set this up.
The trick is to get a few Raspberry PIs and install the software. The NinoTNCs are really cheap so you can make a network on your desk without any radios. Then get the radios after you can con some couple of other hams within a few miles to play with it with you. It's a kick.