They think that autism (and ADHD) are caused by multiple genes, many of which we haven't yet identified. Essentially the theory goes that the more of the genes you have, the more "severe" the autism, and some of them may also sort of be "activated" by environmental factors e.g. lead exposure, birth hypoxia. It's possible to have some genes associated with autism, but not be autistic. It's similar to how someone can have a genetic risk for e.g. heart disease and might need to be more careful about their diet compared with someone else without that risk.
It's more complicated than that, and not as clear cut as diet and heart disease, but as a very simple starting point. It would make sense that a parent may pass on some genes relating to autism and the other parent may pass on some genes and these can combine to result in a different presentation.
But I think you need to look at other factors which are likely to lead to this observed pattern too.
The more impairing a person's autism is, the earlier in life it tends to be recognised. Autistic parents may have DC with milder presentations which aren't picked up until later in life (or at all), but you notice the DC with more impairment.
I remember autistic children (the sibling of a friend; the child of an adult family friend) who were intellectually disabled, so more impairing presentations of autism also existed in previous generations. Those children, now adults, are unlikely to have children of their own, so the order of a more-impaired parent having a less-impaired child is less likely to happen than the other way around. Autistic adults who have children but struggle to look after their children due to their difficulties may also have the children removed or placed with another family member, so again you would not necessarily see this. If you are aware of a child who has been adopted or is in foster care, you would not necessarily know their background.
I understand that autism rates are increasing, and some of this is due to increased parental age (which affects chromosomes) and some is due to higher survival rates in newborns who are born small, early, or don't get enough oxygen at birth. It's possible this is doing more of the "activation" of the genes which have been present through the generations.