I'm not sure I buy the whole syntax argument. I programmed in Forth for a while and it seemed like it was much easier to build up an understandable vocabulary than some of the C++ / Smalltalk class hierarchies I have seen. REBOL has dialects that work fairly well. I cannot help but think that DSLs are refinement of APIs the same way C is a refinement of Assembler.

When I talk to someone about what happens in a system it seems like a DSL flows from that conversation.

"It is to describe how to perform a complex task to other humans in a form that computer can also execute."

I think a DSL does that much better than a set of API calls, particularly when you involve non-developers. That is the point of a DSL.