Always amazing to witness such moments, even if they can look a bit grim to our eyes. (As Tennyson put it, nature is unsentimental, 'red in tooth and claw.')
One thing---with the head looking (to me) capped rather than hooded and with those thicker legs and the bird's overall size in relation to the dove, I'd call this a Cooper's Hawk, not a Sharp-Shinned. Does that feel right to you?---or are you pretty solid on the id?
As you may know, accipiters have been known to use windows in precisely this way: put a prey-bird to flight, get it to stun itself by smacking into a window, and then swoop down for an easy meal. Again, grim, but quite brilliant too. It's essentially a form of tool-use!
Noah