Real shadows behave differently depending on where and how many light sources there are. The sun will cast a sharp, well defined shadow like that on a clear day, but on an overcast day or if you are indoors with multiple light sources the shadows will be softer. Ray-tracing, as someone mentioned, eliminates the need for programmers to code fake shadows because ray-tracing actually simulates light rays as they bounce off everything in the scene. It remains to be seen how this will benefit the gamer/consumer because although it will be less work for programmers, they still have to offer games with the old tricks in them because not everyone will have a ray-tracing capable gpu. It actually might result in a bit more work for them because they have to support both, although with ray-tracing I think all they have to do is define the objects and light sources in the scene which has to be done anyway, and as already stated the hardware takes care of shadows, reflections, refractions, etc. The "tricks" will be enabled for those without ray-tracing hardware and disabled for those with ray-tracing hardware. So as an example with your video above if clouds roll in when you are playing the game, the programmer would have to program the clouds AND program the shadow to change to soft edges, but with ray-tracing hardware they just program the clouds and the hardware takes into account the new objects and their properties which diffuse the source light (the sun) and the shadows will just change automatically.
I tend to think I'm oversimplifying though because what Turing offers is actually hybrid ray-tracing + rasterization and real-time ray-tracing effects will still be computationally expensive and already we've seen indications that developers had to reduce application of those effects in the game (was it BF5?). So, what they might be doing is adding ray-tracing to this or that in the scene, but not everything.