I have gotten this working although my solution might not be as pretty / fluent as it should be.
Variables (I didn't spend a lot of time thinking of a good name for them lol)
ButtonsInteger - This is an integer variable with array size 4 (or however many buttons you will have)
Buttons - This is a dialog button variable with array size 4 (or however many buttons you will have)
Dialog - This is a dialog variable, no array
Untitled Trigger 001
Events
Time - Elapsed game time is 1.00 seconds
Conditions
Actions
Dialog - Create a dialog button for Dialog labelled 1
Set Buttons[1] = (Last created dialog Button)
Dialog - Create a dialog button for Dialog labelled 2
Set Buttons[2] = (Last created dialog Button)
Dialog - Create a dialog button for Dialog labelled 3
Set Buttons[3] = (Last created dialog Button)
Dialog - Create a dialog button for Dialog labelled 4
Set Buttons[4] = (Last created dialog Button)
Dialog - Show Dialog for Player 1 (Red)
EDIT: Cleaned up some unneeded code in there
Untitled Trigger 002
Events
Dialog - A dialog button is clicked for Dialog
Conditions
Actions
If ((Clicked dialog button) Equal to Buttons[1]) then do (Set ButtonsInteger[1] = 1) else do (Do nothing)
If ((Clicked dialog button) Equal to Buttons[2]) then do (Set ButtonsInteger[2] = 1) else do (Do nothing)
If ((Clicked dialog button) Equal to Buttons[3]) then do (Set ButtonsInteger[3] = 1) else do (Do nothing)
If ((Clicked dialog button) Equal to Buttons[4]) then do (Set ButtonsInteger[4] = 1) else do (Do nothing)
Dialog - Clear Dialog
If (ButtonsInteger[1] Equal to 0) then do (Dialog - Create a dialog button for Dialog labelled 1) else do (Do nothing)
Set Buttons[1] = (Last created dialog Button)
If (ButtonsInteger[2] Equal to 0) then do (Dialog - Create a dialog button for Dialog labelled 2) else do (Do nothing)
Set Buttons[2] = (Last created dialog Button)
If (ButtonsInteger[3] Equal to 0) then do (Dialog - Create a dialog button for Dialog labelled 3) else do (Do nothing)
Set Buttons[3] = (Last created dialog Button)
If (ButtonsInteger[4] Equal to 0) then do (Dialog - Create a dialog button for Dialog labelled 4) else do (Do nothing)
Set Buttons[4] = (Last created dialog Button)
If ((ButtonsInteger[1] Equal to 0) or ((ButtonsInteger[2] Equal to 0) or ((ButtonsInteger[3] Equal to 0) or (ButtonsInteger[4] Equal to 0)))) then do (Dialog - Show Dialog for Player 1 (Red)) else do (Do nothing)