TL;DR: "plant" is a role, and this role functions at timescales incompatible with the original requirement. Anything that can move fast and has a brain is an animal, the best you can get is a photosynthetically capable animal - but the energy it could have from photosynthesis would likely be useless anyway.
The problem that you're facing is that anything that is a plant is incapable of high-energy processes, like movement and heavy, real-time processing (and eventually sentience).
What plants do is concentrate the available energy, and other lifeforms use this concentrated energy to support their high-energy processes. The ambient energy is collected, and with its help, some chemicals that are not of much use by themselves are converted into more energetic compounds (more or less). The energy stored in this way can then power those other lifeforms that move around and respond to things quickly. The waste products are then, of course the same chemicals that the plants "energise".
In other words, plants are not as much as specific kinds of organisms as a specific "stage" of the energy chain - one that concentrates the thinned out ambient energy and passes it onto the next stage.
In Earth's case, the plants mostly work on sunlight and beat stuff like nitrogen, water and carbon into sugars and other organics. Most organisms that eat plants in one way or another can then power their own locomotion (excluding obvious stuff like fungi). Most of those are very delicious and get eaten themselves, but they're still mostly on the same stage, the only really efficient energy boost happens with the plants - the differentiation is really between plants and animals here, as even their cell "templates" are different. Either way, the specifics of the plants we have here on Earth are likely unique to Earth, but the role of that first energy stage is not.
This question brings up an interesting alternative, for example - instead of sunlight, motion energy is captured and (presumably) used and stored in a similar way to our Earth's plants - by converting chemicals into other, more energetic ones. Some of the answers detail very interesting specifics of capturing motion energy, but the overall design and idea of the plant is virtually unchanged, except for specific changes needed due to how such energy is distributed, compared to sunlight (direction, intensity, seasonality).
If those hypothetical plants still produced the same sugars (and weren't poisonous), regular Earth animals could probably feed off of them. We could swap out Earth's plants with those alien plants and it would've probably worked out mostly fine, after like a century or two.
Another thing is that most of the reactions happening in plants are fairly slow, both because of their nature as well as because they happen at the ambient temperatures (that's why warm-blooded animals are more capable than cold-blooded ones), and because of the chemicals and rudimentary signals being sent by free flow of fluids. Animals also have systems that work that way - the different hormonal signals and their effects are far, far too slow compared to nervous system response times (even the fastest hormones in humans are on the order of seconds).