Is the term 'allele' specific to sexual populations?
No, it's fine to use for asexuals too. There's an ambiguity in the term "locus" for asexuals, but "allele" is fine, and "gene" is not much more ambiguous than it is for sexuals (which isn't saying much).

Your final paragraph seems confused though, and I think it's related to your main question. When recombination is sufficiently frequent to keep the population in linkage equilibrium, it allows us to represent the population simply as a point in allele frequency space, rather than in the full, exponentially-larger genotype space. So Watson and Szathmary are using different terms for the two cases not because they can't use "allele" in an asexual context, but because alleles are not sufficient to describe an asexual population.

In general sexual populations are not in linkage equilibrium and cannot be simply described by allele frequencies either, as W&amp;S note later in that paragraph.