So you are going to calculate the positions of the simulated spacecraft within your game, to millimetric accuracy, despite that you would need a screen the size of the Earth's orbit around the Sun in order to notice the difference?
No. The point is to use the same numerical object to represent the position of the spacecraft, all the way from take off on ground level to orbit and docking. I don't know in details how exactly using floating point numbers to do so causes problem, but clearly it did cause problems for KSP.
PS. Also, with a program like KSP, you may not have a screen as big as the solar system, but it's just as if. You have a huge range of numerical values that makes a virtual scene just that big.