Yes, that is the correct grapple mutator and NDdj4 is the double jump mutator that you need if you want double jumps.
I guess what might be the problem here is possibly whether you are starting a "listen" server vs. a "dedicated" server. I didn't see in the video if you clicked start or dedicated but try again with dedicated if you didn't already. It's possible that the grapple mutator was made with the assumption it would be running on dedicated servers only.
If that doesn't fix it, you might instead just download one of the full server downloads for your OS and start the dedicated server from the downloaded and extracted server download separate from your installed game (this is how online servers are typically run). It will take more configuration but then will always be there exactly how you made it whenever you want to play on the LAN presuming your computer is powered up and the server is running 🙂
