They do NOT have a peculiar way of showing it. They have a DIFFERENT way of showing it than YOU. That is not a bad thing, just a different thing.
And if you can't understand that, this conversation is worthless.
Well, very different then.
I mean, they state that they are fans of the show and love the characters. Then they kill off one of them, in that case the main character permanently, ruining their own possibilities to come up with great stories in the future about that character and at the same time making many fans of that character sad and annnoyed. Not to mention that those fans might turn their backs on the books as well because of that and that they will be remembered by those fans as "those who killed Janeway and ruined the relaunch for us".
That's a very different way of showing their affection.