No, that's how it is implemented by a compiler; what makes dynamic scoping "scoping" is that it related to how the variables are lexically organized. It is like claiming you are adding "classes" to a language but then merely providing an object-orientation runtime library akin to like, the Objective-C C runtime. You actually could design a system of a bunch of macros in C to have something like classes, but the low-level mechanism is not that. If you wanted to build something that was dynamic scoping in C++ I would (for avoidance of doubt, this is not what I was saying in my original comment) use thread local storage with a global map (and put the name as a string or something, maybe as a C++2y string template parameter) so that you didn't have to define the variable in the global scope. Because what could dynamic scoping possibly mean if you are literally having to type the variable into the global scope?
You really are confusing the implementation of dynamic scoping with what dynamic scoping is: the entire point of having that term at all is to describe how the variables are scoped not how they are set. If you have to type the name of the variable into the global scope, then obviously it isn't dynamically scoped.
The only difference between what you're thinking of and what I'm thinking of is you're row-based and I'm columnar-based. Why is that such an important difference?
The deep binding approach will not work correctly with multithreading any more correctly than shallow binding, if there is only one such stack, or any shared state whatsoever that is not atomically manipulated.
It will work if there is a spaghetti stack. So that is to say, each thread extends the dynamic environment with a newly allocated frame that points upward to the parent environment.
Each thread needs a thread-specific pointer to the top of its own dynamic environment chain.
I'm not sure what you think is the important difference between these implementations?
'Dynamic binding' is an abstract concept. The abstract concept is a global variable with a stack of values. How you implement it and whether you share the call-stack instead of a separate stack is is up to you. It's still the same dynamic scoping.
Only one of them works with multiple threads. Dynamic scoping based on save-and-restore of symbol value slots is completely incompatible with multithreading. That's why Emacs still doesn't have threads.
You really are confusing the implementation of dynamic scoping with what dynamic scoping is: the entire point of having that term at all is to describe how the variables are scoped not how they are set. If you have to type the name of the variable into the global scope, then obviously it isn't dynamically scoped.