Clark et al, 2008 show impairment in ASD individuals for detection of the emotional content of microexpressions.
In general, ASD individuals have trouble discriminating the nuance of facial expressions (though some argue otherwise: see for example Ozonoff et al 1990), for example the differences between genuine smiles and posed smiles (for example, Boraston et al 2008); ASD individuals can learn/train to improve recognition of these cues, however (for example, Solomon et al 2004).
Tardif et al 2007 suggests that slowing down a discrimination task improves performance for ASD individuals, again suggesting that impairments may be worse for briefer displays like microexpressions. This result is also consistent with the idea that, for some ASD individuals, detecting emotions is more about learned rules rather than the more "automatic" emotional detection process for typically developing people.
Overall, I don't see evidence for the claim in the linked article. That said, ASD individuals are each unique humans, and there could certainly be specific individuals who are sensitive to or have learned to recognize microexpressions, but the article doesn't cite any reference. A general caution to be aware of and sympathetic to difficulties with social cues for ASD folks applying for jobs makes sense to me; connecting this to enhanced microexpression detection does not.
(I'd add, also, that the existence, nature, and ubiquity of microexpressions is a bit controversial: see Porter & ten Brinke 2008)
Boraston, Z. L., Corden, B., Miles, L. K., Skuse, D. H., & Blakemore, S. J. (2008). Brief report: Perception of genuine and posed smiles by individuals with autism. Journal of Autism and Developmental Disorders, 38(3), 574-580.
Clark, T. F., Winkielman, P., & McIntosh, D. N. (2008). Autism and the extraction of emotion from briefly presented facial expressions: stumbling at the first step of empathy. Emotion, 8(6), 803.
Porter, S., & ten Brinke, L. (2008). Reading between the lies: Identifying concealed and falsified emotions in universal facial expressions. Psychological science, 19(5), 508-514.
Ozonoff, S., Pennington, B. F., & Rogers, S. J. (1990). Are there emotion perception deficits in young autistic children?. Journal of Child Psychology and Psychiatry, 31(3), 343-361.
Solomon, M., Goodlin-Jones, B. L., & Anders, T. F. (2004). A social adjustment enhancement intervention for high functioning autism, Asperger’s syndrome, and pervasive developmental disorder NOS. Journal of autism and developmental disorders, 34(6), 649-668.
Tardif, C., Lainé, F., Rodriguez, M., & Gepner, B. (2007). Slowing down presentation of facial movements and vocal sounds enhances facial expression recognition and induces facial–vocal imitation in children with autism. Journal of Autism and Developmental Disorders, 37(8), 1469-1484.
Winkielman, P., McIntosh, D. N., & Oberman, L. (2009). Embodied and disembodied emotion processing: Learning from and about typical and autistic individuals. Emotion Review, 1(2), 178-190.