As with all of the Nutri-Net Sante studies, this is very complex. Also similarly, the absolute risk increases aren't very big. I'd be hard-pressed to think of a way that sweetened drinks specifically, outside of everything else that we eat/drink/do, could be linked to cancer
All that being said - there's a strong mechanistic argument for obesity causing cancer, so it's perhaps not surprising that drinking more sugar could lead to worse health. But yeh, not an easy one at all