Spoiler warning!/Explanation of my thinking:
I simply pointed out the story reveals and heavily implies the fact the cast was invited to the Theater. Well, as far as we know, due to limited information.
We know, thanks to Toby in the bathroom scene, that Jack (The protagonist) wasn't given an invitation to the theater. He came on his own accord due to his sister's (Sabrina) suggestion.
Toby revealed in a bathroom scene that: he, Paula and Frederick got an invitation.
Guy's "invitation" came to light when Jack fished his ticket out of his dead body. It had 7 holes (more on that later)
So far we know only: Paula, Toby, and Frederick have gotten an INVIATION. Maybe Guy too, but it's odd because Jack only found his TICKET, NOT an invitation letter. But for now it can be implied Guy was also invited to the theater. Jack found Toby's ticket inside the invitation letter with 2 holes, that's why I assume Guy also has a invitation.
As for the holes on each ticket. Honestly I don't know. Jack had 1 hole on his ticket, Toby had 2, Paula had 4, Frederick had "6" (Toby isn't sure if it's 6), and Guy had 7. We can imply we are missing 3, 5, and maybe 8 (or 1)? These would or should cover Barry, Simon and Philip.
(Keep in mind, Jack was GIVEN a punched ticket with one hole by the snake in front of the Dante Theater. The interaction between them was a bit off, but nothing definitive can be implied or concluded. So maybe someone else has 1 punched hole?)
It's clear they probably mean something, but I don't know enough (or I'm too dumb) to piece it together. Reading and agreeing to a top comment, it could very well be inspired off Dante's inferno layers (Which could also explain the name of the theater "Dante Theater" lol). Which if correct, Guy would be Violence (makes sense), Paula would be Greed (Toby is from a rich family), Frederick may be heresy, Toby is Lust (makes sense...), and Jack would be Limbo (the least punished circle of hell). The part of the novel is called "Paradise" to be fair.
Maybe Simon is 8 holes, the circle of hell for Fraud? False Prophet? He is a pastor at Papillion.
Etc.
I pointed out that the invitations seem very similar to the movie detail in "The Menu(2022)" Where everyone got invited to the location, but the protagonist (Margot Mills) wasn't - effectively kinda ruining the chef's plan. We could compare the Chef from the movie to the Showmaster.
TLDR: The cast, except the protagonist, probably got invited for a reason.
Ooh Dante's Inferno layers corresponding to punch holes could be interesting, then it could get into a bit of like the Saw films where Jigsaw was watching them and gathered those he thought needed to learn a lesson and all that. So i think ur deff onto something there!
Especially thinking of the idea it mirrors The Menu with Jack either A. ruining plans, B. being one to either help the others through potential trials to come (If it ends up like Saw and they represent a different sin) or C. showing The Showmaster that there are some who can appreciate art for what it is and see it's parallels to real life.
Awesome theory crafting there. Can't wait to see what comes next :3