If all of your dimensions are whole multiples of the Blender unit (normally 1m), and aren’t too big (no more than six digits long), then you will be simulating fixed point in Blender and your dimensions should stay nice and even looking. Other than that, yes, in answer to your question: Blender would have to use some kind of fixed point representation for all dimensions to avoid this problem. This would be expensive (in performance terms) and is very unlikely to happen.
The other thing going on here though is that you have transformations, which are implemented by multiplying the coordinates by matrices filled with floating point numbers. When you do what you are doing in this video - changing the coordinate in the global coordinate system, which Blender then has to transform into the local coordinate system of the object, Blender has to multiply by the inverse of the transformation matrix. So even if the transformation in the forward direction looks nice and integer-like (say, scale by 3), the inverse matrix is only going to have exact representations in very special circumstances.