Because AppleScript was designed to be a automation system, as opposed to a full-fledged programming language, it has always restricted its GUI to simple 'alert'-style panels. The idea was that a script should bother the user as little as possible, showing dialogs that ask for a single piece of information and then getting out of the way so that the script could work more or less invisibly. Its native alerts have a maximum of three buttons (on the "Yes", "No", "Cancel" model). The only native way to deal with a choice of more than three items is to use the choose from list command, e.g.:
set meal to choose from list {"Hamburger", "Pizza", "Spaghetti", "Cucumber Salad", "Pork Chops", "Green Eggs and Ham"} with title "Meal Time" with prompt "What do you want to eat?"
which produces an alert like this:

While it's possible to create a multi-button alert with rows of buttons using AppleScriptObjC, it's a non-trivial task: a lot of effort for little reward. Basically one has to create a new alert using NSAlert, then create and attach an accessory-view in which you've added and positioned your rows of NSButtons. You'll also have to add some logic so the accessory view buttons you've created act as 'alert' buttons (meaning they dismiss the alert when clicked). Stack Overflow isn't really meant for coding services — though people do occasionally break that rule — but if you want to work through the bulk of the coding yourself, we'll happily assist you with difficulties.