It's a case-matching study, where they took children with autism and matched them to controls without autism, matching for a variety of factors. This is not the strongest type of study available, but it's an accepted method of doing this kind of thing.
They have compared children who were unvaccinated, vaccinated with the triple MMR, and vaccinated separately for measles, and found that the vaccines appear to protect against autism. The MMR vaccine appears to protect much more than the single measles vaccine, too. The trend shown is very clear, not a slight variation but clear effect.
As this blogger points out, it isn't so likely that the vaccines actually do protect against autism to that extent. If they did, this trend would have appeared on some of the many earlier studies that have been done on the subject. So maybe other factors are at work here, such as parents who detect signs of developmental disorders in their children choosing not to vaccinate. However the main message: that the vaccines don't cause autism, is perfectly clear here, as in the many earlier studies.
(The blog I've linked to above isn't very polite in its opinions of people who promote anti-vaccination. If you are going to be bothered by some strong language on the matter, don't read it. If you are interested in the science of vaccination it's a good one, though.)
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