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.
No, the concept of evil does not impinge on atheist philosophy. In a non-religious context evil can be regarded as originating from, for example, psychopathy, sadism, pathological narcissism. Furthermore, where leadership is psychopathic and/or paranoid conformity and authoritarianism can cause evil - or pathological disfunction - to spread into wider society, (since those not conforming to the pathological worldview would be endangered).