Many "simple animals" like a fly, or a caterpillar or a bee have periods of inactivity that could be an example of rest. But sleep and rest are not the same. If we put brain waves aside, we are left with the behavioral definition of sleep: it is a state of reduced awareness of the surroundings, there will be some latency in arousal, it is reversable, and it is associated either with immobility or at least reduced activity. This study obviously used this definition, so it is not exactly being "tired".
Removing brain waves from the equation, it seems like the whole question of what attests for sleep gets blurry.
Now, with "lower" animals it gets tricky, because all we have is a behavioral definition of sleep. But still, it makes a distinction of reduced awareness, arousal latency. Can we call it "sleep" in these animals, jellies included? Maybe not, maybe it is some sort of proto-sleep state?