The short version - and this is, as the article indicates, disputed - is that the bees catch both a fungus and an RNA virus at the same time, and die. Within the hive, the Varroa mites spread the virus, and the fungus spores spread in the hive vicinity.
And the spread of the virus between hives? That looks to be via the plants being pollinated. If the hives are being transported huge distances (the most obvious example of that is the US, where one hive may end up in a number of different states), then the infection can spread across the country in only a few seasons.