It's implied that the aliens eat, it's just something we never see.
One thing that bugs me about it is how quickly the creatures grow (including the one in Prometheus) very quickly, apparently without eating. In order for a creature to grow in physical size and weight, they must consume something at least equal to that weight that was gained (and generally much, much more). Take the squidhugger for example.. it went from something weighing maybe four or five pounds to several hundred pounds. You can't simply pull that mass out of the ether.. it has to come from somewhere.
In most of the films, this actually gets a pass, usually in the form of the novels or deleted scenes or something. In the first film, it was eating from the ship's stores. In the second, they were eating livestock and stored food. In the third, presumably bugs or other small indigenous life. In the fourth, it's probably safe to assume that the scientists were feeding them. But was there really enough biological material in that medical room on the Prometheus escape pod to feed it? It seemed contained there, unlikely that it got into the food storage.
Just a thought. On the surface, it pretty much matches all the other films, creatures growing very large entirely on their own, it's only when you stop to think about it that you start scratching your head. That, and I just got up and have really bad bed head.