If humans evolved from apes, will the apes of today continue to evolve into a Neanderthal-like species?
Not necessarily, as organisms can evolve in a vast plethora of differing directions from the tiniest of initial variations.
Homo sapiens are but one descendant of a common ancestor that lived 6 million years ago. From that common ancestor, various evolutionary paths emerged, that driven by multiple factors- such as climate change-created multiple new species.
It is a common misconception that evolution is a linear isolated process. Just because homo sapiens evolved from an extinct species of ape, it doesn’t mean all apes will evolve into early humans. This is partly due to the inability to predict future conditions on Earth, but also because natural selection does not always lead to a generation of more complex organisms. On the contrary, natural selection in many cases tends to lead to simplicity, with organisms losing abilities and features that do not benefit their chances of survival. A good example of this is cavefish, which due to their natural environment being deep waters within caves, swamps and lakes where there is little or zero light, have lost their eyes completely.