The route seems to be (lines separated):
Starting at McMurdo, DTN software on a mobile phone sent the picture on its journey to the International Space Station. The bundles traveled from the McMurdo ground station to NASA’s White Sands Complex via the Tracking and Data Relay Satellite (TDRS).
That's an uplink from McMurdo to one or more TDRS satellites, ending in a downlink to White Sands. (If there was more than one TDRS satellite involved, that was via the usual protocols, not DTN; TDRS itself doesn't have DTN support)
Then, a series of DTN nodes forwarded the bundles to NASA’s Marshall Space Flight Center in Huntsville, Alabama, which is the access point to the operational space station DTN network.
That's a series of Internet connections through store-and-forward DTN servers. most likely the connections were terrestrial fiber.
The bundles were forwarded to the space station via another TDRS link where they were then routed to the Telescience Resource Kit (TReK) demonstration payload.
That's an uplink from Marshall through one or more TDRS satellites (see above) to the DTN test equipment on ISS.
The final DTN node extracted the picture data from the DTN bundles that originated from Antarctica. The payload reassembled the original picture and displayed it onboard the station.
It's a mix of terrestrial and space nodes and links.
The terrestrial DTN nodes between White Sands and Huntsville aren't "nodes" in the way we think of e.g. "Deep Space Network node": big communications complexes. Rather, they're probably research servers running test DTN software to act as the DTN equivalent of an Internet router: The thing that's responsible for the next step on the way.
There's been quite a bit of work on using DTN terrestrially, both to link space access points but also for disaster recovery and military purposes:
The basic idea behind the DTN is that to build a disruption tolerant network, you can't rely on any specific link, or even a specific topology of links. The nodes at the bottom of the figure in the Question have disks attached because DTN nodes take responsibility for the bundles (message parts) that they receive; they hang on to them and attempt to deliver them despite disruptions that might take a while. The DTN nodes also attempt that delivery via multiple routes, perhaps not knowing which will succeed and when. (Even the choice of routing algorithms is still in flux) In some cases, they might not even know by what specific route the delivery was accomplished.
Without looking at the logs, it might be that nobody knows which terrestrial nodes actually handled the deliver.
