en kyst = a coast, kysten = the coast, kyster = coasts, kysterne = the coasts
Or do you wonder why anyone would swim along more than one coast? They're probably ultra-endurance swimmers ;-)
They are baywatchers on a tour
Usually people swim along one coast at a time, so, it just sounds odd to say the coasts.
Maybe you and I are swimming along two different coasts?
The y in kysterne sounds more like an ø to me. Is it really the case?
Even if a person swims a long way they are still only swimming down the coast there are not multiple coasts, it is one long land / sea boundary.
It could be plural. Imagine two really keen long-distance swimmers saying, "We visit many countries every year. During our visits, we sim along the coasts." Rather contrived, I know, but possible.