Maybe this is an American thing? In Canada Netflix has Star Wars, Star Trek, Marvel movies, etc. It's not often I can't get something on Canadian Netflix because of an exclusive issue. Game of Thrones might not be on there, but I haven't checked.
Netflix Canada has all the same Disney-owned content as Netflix elsewhere at present (that's Disney/Marvel/Star Wars/Pixar/etc), but won't after the Disney/Netflix content deal expires some time next year. Presumably the Marvel Netflix Original shows like Daredevil would stay, but they weren't part of the larger content deal that's expiring.
Any mention of Star Trek being exlusive to this or that platform would be specifically referencing the current series Star Trek Discovery which is exclusive to CBS All Access in the US, Bell Media's Space and Crave services here in Canada, and Netflix everywhere else. Plenty of streaming services carry all the old Star Trek shows, but the new stuff is being walled off to only one provider in any given region.
As for Game of Thrones that's definitely NOT on Netflix, that's HBO. Bell Media has all the exclusive rights to HBO content in Canada locked up tight, both current and classic.