I'm assuming your Rook does move?
Usually he does, yes

. I haven't had experienced "unusual move blockage" with any Demigod yet (note: "usual move blockage" would be: order not executing yet due to delayed data packets between 2 players; Demigod being stuck at the edge of a corner etc. for a short amount of time; Demigod frozen from the Sludge Slinger/Parasite Egg bug)
Btw, I'm browsing the Rook TOL code atm to see if I notice anything that could cause the target lockup. If you have any additional information about its circumstances I'd love to know it.
So far the teleporting thing, that you brought up, is the only clue I have and I think it's a very good lead on the issue.