The study did not specifically test said products, yet they note future studies ought to do so.

However, given that dairy products do indeed have DNA from the cow they are taken from and are pasteurized at 280-320C, a temperature range far greater than anything tested in this study, it stands that the conclusion could be the same. I am unfamiliar with the specific heating practices in common yogurt brands, so I cannot even begin to speculate there.

This would match up with some initial evidence that cancer, especially prostate cancer, may be linked with higher dairy consumption. However, the authors in these studies speculate that the cancer risk is from high consumption of IGF-1 (insulin-like growth factor 1) which is especially high in dairy products. The linked study looked at direct comparison between soya milk and dairy milk which can be troublesome because soy products have been shown decrease risks of cancer. Other studies comment on the effects of milk on cancer risk from several linked papers.

To gain deeper understanding of whether dairy milk may influence cancer risk, more research is needed to clarify whether there are plausible biological mechanisms, including how different dairy products relate to the IGF system, to other hormones and to other bioactive constituents.

This is especially important with the original post here. There may be future studies that expand on the relative risks of both IGF-1 and damaged DNA in dairy.