Strictly speaking, funcall would not be needed, but there are some lisps (lisp-2 variants, such as Common Lisp) that separate the variable name space of the function name space. Lisp-1 variants (e.g. Scheme) do not make this distinction.
More specifically, in your case, test-func is in the variable name space.
(defun foo (test-func args)
(funcall test-func args))
Therefore you need a construct that actually searches the function object associated with this variable in the variable name space. In Common Lisp this construct is funcall.
See also this answer.