I'm confused by the mention of sex and viruses, perhaps the quote was taken out of context. But is it true that asexual organisms cannot pursue selfish strategies, or to rephrase it, is it probable that no asexual organism has an ESS with a mixed strategy (ie, to sometimes behave differently than its twins)? 

Epigenetic differences due to the environment aside, there's really no reason why clone organisms should pursue selfish strategies at each others' expense. In fact, it was to precisely to explain the existence of seemingly altruistic behavior amongst eusocial insects that W.D. Hamilton first put forward the fitness-maximization theory to begin with: thanks to haplodiploidy, it makes sense for worker ants or bees to devote their energies to raising the offspring of their queen rather than raising their own, as they will be more closely related to her children (75%) than they would any they could bear themselves (50%). The unit of selection in nature does indeed seem to be the gene rather than the organism, so no purpose is served if clones behave selfishly towards one another. See the work of Robert Trivers (e.g. this paper) for some examples of these ideas in practice.