What exact role do higher-order combinators (or function producers) hold in concatenative and tacit programming?
Is there another way to implement a concatenative programming language rather than directly manipulating the stack?
How tight is the relation between the combinators mentioned and Schonfinkel's combinatory logic?
In my answer to "Explain Concatenative languages to me like I’m an 8 year old" I argued that it is not useful to use the word "concatenative" to describe programming languages. This area appears to be a private playground for Manfred von Thun. There is no real definition of what constitutes a concatenative language, and there is no mature theory underlying the idea of a concatenative language. Because the concept is not really defined, it is impossible to provide a definitive explanation of the role of combinators.
You might prefer to spend your time studying more well-established topics such as combinatory logic, SK combinators, lambda calculus, and graph-reduction machines. If you are interested in point-free programming from a more pragmatic perspective, APL, Forth, and PostScript are all well worth studying.