The ropes seem stretchy because the mouse interaction script is infinitely strong and forces the rope to be pulled along no matter its strength. You can take a look at the ropes that are free to swing without the mouse pulling them (the crane for example) for a more realistic scenario. Use the up and down arrow on the keyboard to rotate the drum of the crane. (I should maybe update the demo and make the mouse less strong as quite a few people comment on this)
That said, it's difficult to get perfectly stiff ropes while keeping the simulation stable, there will always be a small amount of stretch. To increase stiffness, one can a) lower the physics time step b) increase the solver iteration count and/or c) lower the resolution of the rope.