the meaning is almost interchangeable. "at" usually implies a specific restaurant (eg. Eat at Joe's, not Eat 'in' Joe's). 'In' implies inside the building. I think the website is looking for a direct translation.
as an english speaker i would never say "the guest eats IN her restaurant" i would use "AT her restaurant" but I agree with nathan, I think the site is looking for a direct translation :)
The correct English translation is "AT her restaurant". "IN her restaurant" is just weird, almost incorrect. And they are rejecting "at her restaurant"!!! I'm reporting it.