SID's are designed for a climb gradient of 3.3% or greater. The standard is 3.3%. If higher is required it will be noted on the SID chart.
I assume that you are flying a twin engine a/c. The climb gradient you are required to meet on one engine is 2.4%. (That's what you are looking at in the climb section of your runway analysis chart.)
You have no business following a SID on one engine unless your performance dept. has assessed that particular departure and confirmed that 2.4% will keep you safe.
Depending who does your charting, it is generally assumed that you will fly straight ahead on one engine or follow an escape route if 2.4% gradient isn't safe on runway track.
It may be that the higher gradient that you refer to is for ATC seperation and not for terrain, but without doing some engineering work you won't know.
In any case, ATC does not necessarily expect you to follow your assigned SID if you've lost an engine. That's why you give them the Pan or Mayday call.
Talk to your performance dept. You really need to know what they've based their performance calculations on. They've made certain assumptions about what you will do in the event of an engine failure. Make sure you're on the same page they are.