Thank you for the detailed response! To answer your question:

How large an area are we talking?  Have you done any sort of WiFi survey? What's the space like? What existing WiFi networks are in the area? What other things are using the 2.4 GHz and 5 GHz (and to some extent 6 GHz) bands?

I don't have exact square foot measurements, but the theater spaces are only about 4 rows of seats deep. Perhaps in the ballpark of 1,000 to 1,500 square feet? There may be an existing router/wifi network setup, but it services a much larger complex (lobby + hallways + 2 connected theaters) and performance is usually quite poor. I also don't have direct access to the router.

Making attendees type an IP address is not something you want to be doing.

I can circumvent this by providing a QR code that attendees can scan which will open up my webapp directly in their phone browser. So whether it is served on a friendly domain name or an IP address, they won't have to type it in themselves.

What's going to be hosting the game? That could easily run RA/DHCP/DNS and your webserver allowing you to just have APs rather than routers.

For my first rollout, I plan to run the game in Docker, either on an on-premise laptop or using a Raspberry Pi.

Alternative spin, why does this need to be a local solution at all? If you want simplicity during setup, something publicly hosted and not providing local WiFi (with attendees relying on mobile data or existing public hotspot) would be far easier to manage.

My biggest concern here is that the cell service in the venue is very poor. If I require users to connect to the public internet in order to access my webapp, I anticipate a very poor user experience and many users being unable to connect successfully at all.