I have terrible dark circles under my eyes and have just ordered facelift eye gym! How effective is this in treating my dark circles?

Not effective. Creams have just not been shown to treat dark circles.
Dark Circles. No this sort of treatment will not have a significant corrective effect and is more hype than truth. Prescription lightening products and blepharoplasty surgery can help many. https://pacificcenterplasticsurgery.com/procedures/face/eyelid-lift/.
Not effective. No products, beyond makeup will improve the dark circles under your eyes unless they are caused by allergies or other medical conditions. Then antihistamines or nasal steroid sprays to control the allergic symptoms may help.
Effective for seller. But unfortunately, this will do absolutely nothing but lighten your wallet, and perhaps increase your wrinkles from all the facial muscular activity. See a plastic surgeon for things that really work, like hydroquinone therapy, periorbital peels, or eyelid lift surgery to remove the bags that cause shadows! send the eye gym back and hope a refund is coming (or deny the credit card charge).
NOT. Unfortunately most things that sound too good to be true, are. Fillers, peels, and concealers (and temporarily, preparation h!) can help with dark circles. When surgery is needed, no product will take the place of the proper treatment. Stop wasting your money and go for a consultation to an experienced surgeon to see what options will impact your eyes! good luck.
Probable waste $. Is this where you train your eyelids to do pushups? All kidding aside, usually excessive muscle action will make wrinkles even more pronounced. I am not sure that this will be effective.