What means that the tor router (in this list) is not mark as "exit"? And is it still possible to contact other onion nodes directly through it (e.g. such that it'd be the node directly preceding the one you want to dial through .onion address)?
If I understand your question correctly:
A nonexit node does not connect to websites outside the Tor network. It will only connect to other nodes or the computer connecting into the Tor network (if it is an entry node). These nodes are often run by people who want to increase the Tor network capacity but not deal with the difficulties caused by people performing illegal activites over the network.
Connections to hidden services aka .onion sites don't use exit nodes. Both the client (you) and the hidden service site build Tor circuits to what's called a rendezvous node. So traffic between you and .onion sites never leaves the Tor network.