I will agree that considering feasibility is important for programming a video game, but game design is not limited to that. It's scope can apply to almost anything, including board games, or even a conversation with a friend where you both co-design some sort of established response to a stimulus.
i.e. 'Slug bug!' when you see a Volkswagen and then you punch them if you called it first. I have heard an amendment where getting the license plate nullifies it. That is game design.

You 'implement' that into your own head. It is a game of thought and mutual agreement.

So saying that you cannot conceive a game purely in your head or that it is useless to do so is pure non-sense.