Question: Does the existence of evil impinge on atheist philosophy, such that it could be seen as a "problem" with, and not just within, these philosophies in a similar way too theism?

Could e.g. Marxism be seen as a response to that kind of dilemma?

Answer: 
The Problem of Evil exists in theism because theists need to provide an explanation for how evil can exist in a world created by an infinitely benevolent deity. Since atheists deny claims about the existence of said deity, the problem simply does not exist. The existence of evil does not by itself present a problem to atheism.
The problem of evil does not just arise in theism and deism, but also in e.g. Hegel's absolute idealism.

Whether or not the left Hegelians have the same problem.