This isn't a solution to the question you're asking, but you might consider selecting "Force Response" for the Text Entry Validation in the Other response option. That way no one could leave the field blank if they select Other.
If you need to allow respondents to leave the Other field blank for whatever reason, then I do not know of any way to customize the Loop & Merge functionality to disable the next question.

In addition to forcing a response, you could also create a branching validation in the survey flow so that if they select "other" and it is empty, you can branch them to ending the survey (or whatever you want the next step to be). You can see the logic below in the image. I assume you have the logic already set up so that if they do fill it in with something it takes them to the next question and pipes that text in, and if they select a different option entirely it takes them to the appropriate question. So you can just merge this logic with it.