As this study is observational, it cannot determine cause-and-effect. Only randomized controlled trials can do that, but we cannot deliberately control who gets infected and who doesn't.

But at least this study managed to rule out the possibility of reverse causation, i.e., pre-clinical neurodegenerative diseases increasing the risk of infections rather than infections increasing the risk of neurodegenerative diseases.

The EBV-multiple sclerosis study, however, provides strong causal evidence of EBV causing MS, despite its observation nature. I described it why in a previous article (link here). And the present study managed to replicate the EBV-MS association.

So, to answer your question, yes, the data is merely correlational. But there's some evidence suggesting a causal nature.