As a kid, I was marginally decent at competitive math. Not good like you think of kids who dominate those type of competitions at a high level, but like I could qualify for the state competition type good.
What I was actually good, or at least fast at, was TI-Basic, which was allowed in a lot of cases (though not all). Usually the problems were set up so you couldn’t find the solution using just the calculator, but if you had a couple of ideas and needed to choose between them you could sometimes cross off the wrong ones with a program.
The script the author gives isn’t a proof itself, unless the proposition is false, in which case a counter example always makes a great proof :p
I used to do the same thing. I'd scan for problems on the test amenable to computational approaches and either pull up one of my custom made programs or write one on the spot and let it churn in the background for a bit while I worked on other stuff without the calculator.