After seeing no one answered what is clear to my eyes and is so simple, the answer is so simple though no one here noticed ><
When you follow the events in the anime/manga, this isn't really a question:
1 - Rem gives Misa Geluss's Death Note.
2 - When Misa meeting Light, she's handing Light her Death Note - from now on Rem's Death Note is in Light's hands, Misa never get her Death Note back before being confined by L.
3 - While being confined by L, Misa is forfeiting her Death Note that Light's holds at the moment, making Light the owner of the notebook.
4 - Light is giving Rem's notebook to give it to Ryuk and then burry it for Misa, because that notebook was in use by Misa, so after Light's memories back she would touch that Death Note and her memories will return.
5 - After Higuchi's death, Light telling her to go dig the buried Death Note so her memories will return. Only now her original Death Note returns to her possession.
Let's now review the threat from Rem to Light:
In ep14 when Light threaten Misa he will kill him she's telling him - "I won't let you do it Yagami Light, If you will kill this girl I will write your name in the notebook and kill you. I can see her lifespan. If she'll be killed before her end I will think that you are the killer."
Now, as other specified there's this rule:
How to use XXXIV
- The owner of the Death Note cannot be killed by a god of death who is living in the world of the gods of death.
- Also, a god of death who comes to the human world, in the objective to kill the owner of the Death Note, will not be able to do
- Only a god of death that has passed on their Death Note to a human is able to kill the owner of the Death Note.
From the look of the rule, the rules doesn't apply to other human but to other shinigami that cannot kill, check this Q&A that kaine proved that other human can kill other Death Note holder though other shinigami cannot kill them.
What that has to do with here? Well, as I explained Misa borrowed Light the Death Note that Rem gave to her, Rem clearly specified that if she'll be dead before her lifespan will be over - she'll kill Light, as Light is now the holder of the Death Note he will be the owner of it after killing Misa and since the Death Note used to be Rem's notebook she'll have the same power as Ryuk has to kill him since she passed the Death Note to Missa, though Rem didn't gave it to Light since Missa only borrowed it to him it's still considered Rem's old Death Note and to her to kill him. So the answer is clear that her threat was real and the things really simple and clear.
Though you could go and say it isn't true since in the end Rem hasn't gave it to him, though to be foolish claim, the evidence for that is the need for Light to give Rem the Death Note when forfeiting it because she also needs to follow Light for using the Death Note, her former ownership of the Death Note didn't stopped when Missa borrowed it to Light 'till he forfeited it.
As for other places as mentioned in this Q&A, Rem could kill Light after he killed higuchi since Rem gave Higuchi Ryuk's former Death Note since she's the shinigami of that Death Note now, now Light is again own Rem's Death Note she's able to kill him since he gained ownership of the notebook after holding it while killing Higuchi so Light considered the ownership of that notebook.