Interesting research but very early stages. There's a good chance that this isn't really specific to bikes, but more generally applies to the benefits of people enjoying hobbies and a good quality of life translating into a better psychological state, which is known to affect health outcomes in a myriad of ways specially related to brain function and hormones.

The data also shows that mixed-walking is associated with reduced dementia as well... and I find it a bit confusing that the authors are lumping driving and public transit together in the nonactive category because public transit usually involves a good deal of walking too without people categorizing it as a walking mode of transport.