if you buy it on your account, all you have to do is loggin into your account, and it realizes that you payed for it, and can download it onto the other computer.
otherwise, good luck actually finding the videos in the itunes downloaded mess folders
yup they’ve both got it nailed – you can, you just have to authorize the new machine (you can have up to 5 authorized). to do that, go up to advanced & click Authorize Computer. it’ll ask for your Apple ID & password & thats it.
if it’s an iTunes+ video, you can put it on as many computers as you want without registering. Just move the file. If not, move it and register. But like they said above, only 5 machines can be registered for an account.