They’ve lost the plot, unless you happen to live at the seaside, which the majority of the country doesn’t, who associates amusement arcades and seafront promenades with Christmas?
I don't think that's the point.
The seaside/funfair location gives two very different connotations. It's a place of fun and getting together with people, but it's also a very sad location. An out of season seaside resort or deserted funfair is a very depressing place, but at the same time it has a certain appeal and romance to it.
That's the juxtaposition - it's both a place of happiness and a place of sadness... the two emotions that the characters go through. Christmas is the thing that brings them together.
You're not meant to associate the seaside with Christmas, it's Christmas that brings the two together. The location is incidental, but chosen because of the emotional extremes it has.
Anyway, that's my reading of it after one viewing