according to the Ball canning book (paraphrasing)...
JAM is made by cooking crushed or chopped fruits with sugar, and is made of one fruit or a combination of fruits, is spreadable, and is firm but will not hold the shape of the jar.
JELLY is made from juice strained from fruit, usually prepared in a way to keep it crystal clear, and is gelatinized enough to hold is shape when removed from the jar, yet is still spreadable.
PRESERVES are fruit preserved with sugar so it retains its shape, is transparent, shiny, tender and plump. the syrup generally has the consistency of honey, and a true preserve will not hold its shape when spooned from the jar.
to add to the confusion, i'll also add their descriptions of...
CONSERVES, which are jam-like and made of a combination of one or more fruits, nuts and raisins, cooked until it rounds up on the spoon.
MARMALADES are a soft jelly containing pieces of fruit and peel evenly suspended in a transparent jelly. similar in structure to jam.
It sounds reasonable: the large quantity of vinegar will acidify the pickles, preventing the growth of botulism.
The processing step is mostly to seal the jars; the vinegar is the real preservation agent.
Still, I would feel better if The Kitchn had cited the source of the recipe, as you only want to use recipes that come from a trusted and qualified source.
Best Answer
In terms of killing pathogens, it is a belt and suspenders thing.
The additional processing ensures that any pathogens that entered the jars while you were filling them are killed.
More importantly, as Jefromi has reminded us, the additional boiling with the assembled and lidded jars causes the header air to heat up, expanding in volume and raising the pressure, and so some of the air will bubble out past the seal. When the jars are cooled, the header air also cools, creating a partial vacuum, and pulling the lid down against the jar. This is what makes the permanent seal--the ring is only there to hold the lid in place long enough for the processing.
So the processing is necessary to seal the jars, even if the food is already rendered perfectly safe from pathogens.
For more information on canning safety, see NCHFP's processing guide.