That definition is at best imprecise and at worst inaccurate. The discussion page even shows someone objecting to that definition for the very same reason we are having this discussion.

The terms predator and prey are defined to describe predator-prey relationships, which are distinct (though similar) relationships to those of a cow eating grass or a bunny eating a carrot. Your definition of prey would include every single organism on Earth and necessitate a definition of predator that would include nearly all heterotrophs, excluding only some decomposers. Such definitions wouldn't be useful.