This is behaviour trees. What you’re describing is behaviour trees. Edit: I see later you say it isn’t a behaviour tree but this is how a lot of BTs are implemented. They don’t always loop from the root. A lot of the time according to state the root is redefined off of a branch and that sub tree is looped until going further down the tree or even into a different tree. Much like the stack you are describing.
The article has been updated in response to this post.
(See the end)