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: 
A couple of references might be apposite here:

1. Both Arendts *Totalitarianism* and *Eichman in Jerusalem* where she examines the nature of Stalins Soviet Union & The Nazi Regime, and also the trial of Eichmann, the Nazi war criminal in Jerusalem; the second book is where she coined the phrase 'banality of evil'. Arendt, was famously a lover of Heidegger; she was also Jewish but highly secularised.
2. Mary Midgeleys *Wickedness:a philosophical essay* is by a Christian philosopher, but in this essay, as this [review](http://www.the-philosopher.co.uk/reviews/wickedness.htm) acknowledges distances the topic of 'evil' from her theological concerns; hence, of course, wickedness rather than evil. To quote from the review:

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> In an area where little recent philosophical work has been done, Midgley's approach combines recourse to ancient sources (Plato, Aristotle, Manicheanism) with reference to more modern approaches, most notably the work of Hannah Arendt. Midgley also refers extensively to developments within evolutionary theory. Midgley's own philosophical perspective on wickedness, however, remains resolutely Aristotelian throughout. On the one side, she vehemently rejects a dualism which would see evil as a privation and something extrinsic to being.
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The etymology of *[Evil](http://www.etymonline.com/index.php?term=evil)* is revealing:

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> Old English yfel "bad, vicious, ill, wicked," (cognates: Old Saxon ubil, Old Frisian and Middle Dutch evel, Dutch euvel, Old High German ubil, German übel, Gothic ubils)
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> Evil was the word the Anglo-Saxons used where we would use bad, cruel, unskillful, defective (adj.), or harm, crime, misfortune, disease (n.). The meaning "extreme moral wickedness" was in Old English, but did not become the main sense until 18c.
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One might say that the secularised notion of evil is returning to its Anglo-Saxon roots.
There are many philosophies for which the existence of error, including moral error, is a problem. These philosophies are justificationist philosophies that claim it is possible and desirable to show ideas are true or probably true. The problem is that if such a method exists then it is possible for people to learn whether their ideas are true or not and so explaining error, including moral error, becomes difficult. Almost all philosophers, secular or religious, are justificationists and so have trouble explaining moral error, including evil.

These problems need not arise. Justification is impossible, unnecessary and undesirable. If you assess ideas using argument then the arguments have premises and rules of inference and the result of the argument may not be true (or probably true) if the premises and rules of inference are false. You might try to solve this by coming up with a new argument that proves the premises and rules of inference but then you have the same problem with those premises and rules of inference. You might say that some stuff is indubitably true (or probably true), and you can use that as a foundation. But that just means you have cut off a possible avenue of intellectual progress since the foundation can't be explained in terms of anything deeper. And in any case there is nothing that can fill that role. Sense experience won't work since you can misinterpret information from your sense organs, e.g. - optical illusions. Sense organs also fail to record lots of stuff that does exist, e.g. - neutrinos. Scientific instruments aren't infallible either since you can make mistakes in setting them up, in interpreting information from them and so on.

We don't create knowledge (useful or explanatory information) by showing stuff is true or probably true for reasons so how do we create knowledge? We can only create knowledge by finding mistakes in our current ideas and correcting them piecemeal. You notice a problem with your current ideas, propose solutions, criticise the solutions until only one is left and then find a new problem. In this light it is unsurprising that people make lots of mistakes. There is no single method that will avoid all mistakes.

See "On the sources of knowledge and of ignorance" in the book "Conjectures and refutations" by Karl Popper.