I'm editing a video with some romantic songs, and I want to name it "For those moments when/that words aren't enough".
"Those moments" is an expression of time; "when" is a pronoun that refers to time. It's the appropriate choice.
You didn't ask, but similarly: "For those people that/who appreciate romance"--which pronoun should I use? Obviously, the pronoun that* refers to people: "For those people who appreciate romance."
(*See what I did there?)
Use "when", without question. That is what I'd definitely use.
I agree with the others that when is the word to use.
That title will work because people will know what you mean, but you are talking about editing a video for those moments when words won't be enough. Your product must be ready in advance for those moments when it will be needed. That moment is not now or when someone gets your work, so a future suggestion of won't instead of a present suggestion of aren't, but people will know what you mean.