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.
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.