Just a bit of background - 95% of humans will experience infection with EBV at some point in their lives. Once you're infected, it remains latent, only flaring up in particular circumstances. MS is an autoimmune disease, like many others, and this paper does not imply that EBV directly causes MS. Obviously, as so many more people have EBV than have MS, EBV infection does not completely explain why people get MS.
Just to put a small caveat to the paper. The comparison is to EBV 'seronegative' population - this is a minority of people (i.e. people who do not have evidence of being infected with EBV). You could argue this is an 'unusual' population in the first place and there's something about them that provides protection from MS.
Another point is that EBV is a risk factor, there are other risk factors known too. I think the key to understanding a lot of autoimmune diseases is to understand how our adaptive immune system works. Our immune response is a very complex cell-to-cell interaction between millions of cells all with different roles, and how the immune system decides whether something is a threat or not is not, and how to respond to it, is not yet clear.