Judging from the location of the blood stain, it would appear he did take a step or two. The blood stain is adjacent to the arm of the sofa. If he were seated, then stood up and got shot, I'd expect the blood stain to be towards the center of the sofa, if not closer to the window. I've tried in a very amateurish way to draw that here, the blue circle showing the general area of the blood stain.
Ignore the dining table as in this Southside Flats brochure photo, he didn't have one. If he were "charging" her, he had a long ways to go to go across the room and around the kitchen counter. More likely, he stood up took a step or two as he was saying and/or thinking "what the f*?" Which is IMO the natural reaction one would have to someone barging in their apartment.