You are not doing anything wrong. You have to download rentals from iTunes - You can't stream them.
There are other apps that will let you stream movies - As you know NetFlix is one, Hulu +, HBO GO, many of the major TV networks have apps that stream movies. iTunes does not stream, you must download the movies.
Thanks Damon. I find it interesting that with streaming being so popular and more & more commonplace, that a site (AKA biz center - income stream) as iTunes in all the years & income it generates hasn't developed $ implemented the ability to strem on demand it's movie rentals.
I don't know the tech involved, but since other sites allow us to view as we "download" why can't/doesn't iTunes I wonder...
Well I think one of the reasons that iTunes will not allow you to stream a rental movie is because the time starts on the 24 hour clock as soon as you start to watch the movie. If for some reason there as an interruption in the download/streaming of the movie.... an interruption in your Internet connection or a power outage, you might be out of luck, once the movie started to download again.
Where I live, we have power outages way too often for anyone's linking and sometimes the outage can last for hours. If I started watching a movie as it was downloading and the power went out - and I had to go off to bed because I had to get up for work the next day, I could burn out the 24 hour limit on the time that you get to watch the movie before I had a chance to finish watching the movie.
If your Internet service was down for any length of time, the same thing could happen. You burn up the 24 hour timer before the movie finishes downloading. These might seem to be unlikely scenarios, but it could happen nonetheless. And it is only my own half baked theory anyway, because I have no clue why Apple does it this way, but it does make a certain amount of sense to me.