A)It bends easier. A round HDMI cable is thicker and cannot bend as easily as a flat one. This makes it easier to install into/along walls.
B)It's easier to tuck behind a hanging HDTV. A round HDMI cannot be wrapped up as tight as a flat one can, and will tend to bulge from behind the television.
C)You can hide it behind a baseboard better. It lays flat against the wall and this lets you put the baseboard back flush without gaps.
D)Running it under carpet is easier. Just make sure you don't put it in under the carpet in a high traffic area. This is something that installers are doing these days since the cable with not cause a bump in your carpet.
E)It can be painted easier than a round one can. This is a huge advantage if you decide to run your flat HDMI along the top of your baseboards and paint it to blend into the wall.
F)Flat design provides less interference and better picture