The result is stored as a single matrix indicating the total cost for the path between any two nodes. Reconstructing the paths from this information is very easy.
Yes, storing ONLY the optimal distances between all paths is relatively small. But often it is also nearly useless by itself.
Reconstructing the paths is not always "very easy" as you blithely commented. For scenarios such as a small game level's map it can be easy, but for other scenarios it can require significant processing; for moderate searches it can become something that is no longer approachable realtime in a game, or outside of games becoming something that is an hours-long process.