Looking at the topography, the airport is surrounded by flat land. Therefore, I am assuming the required climb gradient is for noise abatement. Maybe some towers around the airport area...
For a twin especially, there can be close-in obstacles which are significant in the engine-out case, even though they do not look to be much above the surrounding general level of things. Also, look about 8 nm N of the field, there is a TV tower at 1501 ft amsl. In the days when I flew B737/757 out of BHX, we had a 2-stage emergency turn procedure to follow for engine failure after V1 when using RW 33. The first stage was to go about 15 degrees right to avoid some close-in obstacles, the details of which I forget. The second stage was to miss the TV mast.
Back to your original question, noise abate does not apply to engine-out ops, as I recall, though I am not able to quote a specific regulation.