Recall that the concept of 'heirs' is not alien to elves...but not all that pertinent, either. It's not a question of needing an heir. For instance, Finrod was king of Nargothrond when he met Bëor, and he's still king of Nargothrond when Beren, Bëor's great-great-great-great-grandson comes to visit 120 years later. So, yes, Orodreth is Finrod's nephew. Finrod's brothers are dead and he has no children. Orodreth is, therefore, heir apparent, and also currently at court. But there is no assumption that Orodreth would take over if something were to happen to Finrod - Celegorm and Curufin are banking on taking over themselves.
But more importantly, no one other than Finrod thinks that anything is going to happen to Finrod. Finrod has survived multiple battles already, and he's currently safely at home in Nargothrond. He founded Nargothrond. He has always been king of Nargothrond. There is no reason to think that Nargothrond would ever have any other king. Finrod leaving to go on a quest doesn't mean he won't be king - he has gone on many journeys since the founding of Nargothrond. Finrod takes off his crown at the end of Episode 5 because he realizes his people do not support him. He is not actually their leader any longer. He has been usurped, and takes a 'fine, then' approach to that situation.
In other words, Finrod abdicating the throne and placing the crown on Orodreth's head before leaving on the quest is a surprise to everyone. Celegorm and Curufin were building up political power, in the hopes of commanding Nargothrond's military forces. They were not under the delusion that either of them would be named King of Nargothrond at any point! But Orodreth is an easier elf to maneuver around than Finrod was, so this development suits their purposes.