I don't mean to be sarcastic about the findings reported by Lena McCue and colleagues  talking about how gastrointestinal (GI) dysfunction might show an *association* with sleeping problems in the context of autism. There was however, an air of 'inevitability' about such findings that has been discussed previously in the peer-reviewed science literature (see here)...
Researchers drew upon data from the Autism Genetic Resource Exchange (AGRE) research program (something that they've done before) to identify over 600 children and young adults diagnosed with "idiopathic autism spectrum disorder, aged 2-18 years" (idiopathic = autism not secondary to a known genetic condition). They examined data on the presence of GI and sleep issues in order to gauge whether there was any relationship between the two.
Lo and behold: "The adjusted odds ratio for sleep disorder among those with gastrointestinal dysfunctions compared to those without was 1.74 (95% confidence interval: 1.22-2.48)." Results held even when various potentially confounding variables were taken into account. Ergo: "Early detection and treatment of gastrointestinal dysfunctions in autism spectrum disorder may be means to reduce prevalence and severity of sleep problems and improve quality of life and developmental outcomes in this population."
Gastrointestinal (GI) issues are very much over-represented when it comes to autism (see here). I'd say that the evidence is pretty overwhelming for that last statement both when it comes to functional bowel issues such as constipation and/or diarrhoea (see here) and also risk of more pathological conditions too (see here). Indeed, we've had peer-reviewed published guidance on screening and treating bowel issues in relation to autism  for some time now. Sleeping issues are also over-represented in relation to autism (see here). Alongside seemingly greater risk for specific sleep issues (see here for example) accompanying a diagnosis of autism, sleeping problems often feature as one of the more 'quality of life draining' aspects in relation to autism  (as they also affect significant others too ). It strikes me as a win-win situation that detecting and treating GI issues may also have positive implications for sleep issues in autism.
And finally, a small (peer-reviewed) contribution to this area from yours truly ...
 McCue LM. et al. Gastrointestinal dysfunctions as a risk factor for sleep disorders in children with idiopathic autism spectrum disorder: A retrospective cohort study. Autism. 2017 Nov;21(8):1010-1020.
 Buie T. et al. Evaluation, diagnosis, and treatment of gastrointestinal disorders in individuals with ASDs: a consensus report. Pediatrics. 2010 Jan;125 Suppl 1:S1-18.
 Kuhlthau KA. et al. Associations of quality of life with health-related characteristics among children with autism. Autism. 2017 Jul 1:1362361317704420.
 Tilford JM. et al. Treatment for Sleep Problems in Children with Autism and Caregiver Spillover Effects. J Autism Dev Disord. 2015 Nov;45(11):3613-23.
 Whiteley P. Food and the gut: relevance to some of the autisms. Proc Nutr Soc. 2017 Sep 26:1-6.