I believe Eliezer uses this as a definition of intelligence, but it also works as a definition of agency: to paraphrase, a system that acts to attain or impose a pattern, criterion or constraint on future states of the world.

A crucial metric, IMO, is the degree to which paths of action to these criteria extend from the agent. For instance, a Spot robot acts to maintain the criterion of upright position on its future stance by action of leg movement. This only affects the robot directly through short plans and so is relatively harmless. In comparison, an ASI running on an AWS datacenter may impose the criterion that the datacenter continue to exist, through long chains of action involving the eventual death of all humans intending or posing a chance to destroy it. That would obviously be quite a lot worse, but I think the example illustrates how "imposing a criterion onto the future" captures the essence of agentic behavior at various levels of power and danger, without pulling in any unnecessary detritus such as "consciousness", "will" or "emotion".

I don't have a good definition of agency, but I do think agency is required before consciousness. I believe consciousness is the recognition of how your agency influences yourself and the external world. Having some mental model of the consequences of your own agency.

The dictionary definition is just the ability to take action over something. It sounds like you are using a definition that relies on consciousness which is a much more complicated and vague concept.

For example, I think most people would agree that my pet cat has agency. It can go wherever it wants in my home, eat whenever it wants, sleep whenever it wants, etc. Whether it has consciousness is a much more controversial topic. Basically everything living has agency. Even my houseplant will direct its leaves toward the sun, but few would argue it has consciousness.