Could it be the long term effect of this diet as opposed to ageing?
I believe they are saying both, though I read the article quite a while ago. They talk specifically about a low-fiber diet, which fits with your mention of processed foods. Many unhealthy things you do to yourself when younger don't show their harm until you're older. I believe they're saying this is one of those.
The more I learn about the gut biome the more it seems to connected to a lot of unfortunate outcomes.
The lack of fiber seems to be one part of the story. The over use of antibiotics seems also to be a part of the story. One presentation by a gut biome researcher pointed out that she no longer worries about her kids eating things right out of her organic garden without washing them first. Her advice to her kids is knock of the dirt and eat. That is a way of getting a wider variety of micro biome into the gut. Her research found that the hunter gathers in Africa had the most diverse gut biomes of any group that she studied.
One issue is that the primary source of the gut biome is from the birth passageway of the mother. If mother doesn't have a particular bacteria then her child is not likely to have it either. Of course that deficit gets passed down.
It appears that as a society were are slowly reducing the gut biome diversity of the population and there doesn't seem to be much in the way of restoring that diversity going on.
Anavex found that 2-73 changed the prevalence of certain bacterial groups in the gut of AD patients moving the populations towards that of people that don't have AD.