What country are you in ? Films can't be re-downloaded in all countries (and even where they can be, not all film studios have agreed to it, and they would need to be still in the store)
What can be re-downloaded where : http://support.apple.com/kb/HT5085
Correct, you will need to copy it from your other computer to it yourself and add it to its iTunes (File > Add To Library) - though this page talks about music, you should be able to use the same processes for films : http://support.apple.com/kb/HT4527
Thanks for the info, I am also in Germany and had the same problem.
So much for Apple's claim, "buy once, play anywhere".
Seems, I'd be better off in Nicuragua, than some underdeveloped country
But I can confirm that you can move a film from one computer to another
and add to iTunes library, have done that once or twice before.