Assuming you used the original source code to derive the detailed spec, then yes, that too is a derivative work.
The "viral" nature of that sort of license has bothered me for a long time. It's always been simultaneously overly far reaching and impossible to realistically enforce.
But here's an interesting question:
If you do not execute the code - did you accept the license? Does simply reading it sufficiently to be able to write a spec bind you to that license? That seems a bit too much.
I'm not sure "closed" is the right word. Clearly it's not closed if you are providing it - it's right there, I can read it and even redistribute it without burden.
It's "copyrighted", not closed. You can't modify closed source because you don't have the source. The assertion being made is you can't modify GPL'd open source without accepting the license. But copyright has its own carve-outs, and I am unconvinced that writing a spec or net-new code is a modification, as opposed to regular old copyright fair use.
It's about how to reproduce the functionality - the code could be an entirely different language.
And - "commercially compete" with someone giving away code for free seems a non-concern.