Were the three Resources around the fortress (Mine, Lumbermill, Farm) all currently either under attack or in enemy hands?
A fort is cut off from the Transitus Network unless at least one of the Resources is "safely" in your own side's hands - that means that it has to be held by you, AND not currently under attack.
This being Chalman, and you apparently being Aldmeri Dominion and a long way from home, my best guess is that all three Resources were either held by the Pact or Covenant, or under attack from one or other faction (Chalman being a Covenant / Pact border fort).
Looking at the mini-map above, in your picture: The only Resource in your picture, the Mine, is under your control, but also under attack. The Lumbermill and Farm are outside the mini-map picture, but they are probably in enemy hands already, so there is no way out of Chalman by teleportation, and also no way to teleport in.
Next time, make sure your Resources are securely in your hands.
But I was standing there few minutes, and the transitus shrine was "not clickable" all this time, I could not open the map via activating the shrine. I think I should be able to open map via Activate even without any available jump points connected, right?
Here for a few minutes a single point was available as a green line indicates on minimap.
I have a stable 100 fps, latency 70 playing via fibre cable 600Mbit with a fast SSD 970EvoPlus. I read that in Cyrodiil latency 70 is very good and guarantees no slowdowns. I guess it can't be connection issues, rather something wrong with this particular shrine at the time being.