This context comes from the movie "Get Out" by Jordan Peele
The person speaking is saying this because there was an incident involving that person during this social gathering and now he informs others that he will retire to another room for rest.
"Well, I'll have to let you all get on the rest of the night without the aid of my marvelous wit"
Two suspects I've in mind:
get on
To fare, cope, or manage. We've been getting on well ever since my husband got a new job. Let me know how you get on at your new job.
get on
- To make progress with something; continue something: Stop complaining about the work and get on with it. I'll get right on your request!
Does it mean that they will have to continue the rest of the night without the aid of his marvelous wit or to manage(to be entertained for example) for the rest of the night without the aid of his marvelous wit?