I like minibb's ability to have a forum where non-registered "guests" can post. I tested that on your trial board where you had such a forum, which allowed a guest to just enter any name (which hadn't been taken) and post.

But, to prevent spammers, I would like to be able to have a "real person" test question (like, "What's the last name of a golfer named tiger?" or whatever question I would decide) which an anonymous poster would have to answer prior to being able to post. This is to prevent robot posting. I have used such a "real person" test on a guestbook that is open to posting by non-registered users and it worked well to stop bots from posting.

Is such a mod available? Or is this a feature already implemented?

I am aware that you have a catcha mod which is discussed here:

https://www.minibb.com/captcha.html

And I will indeed purchase that captcha mod (that is very reasonable pricing) even if there is a "real person" test question mod available. But, I have used both approaches and I prefer the real person test question to captcha. Captcha codes get read by machines, but cleverly phrased real person questions prevent spammers much more successfully.

So far I know our codes is very difficult to read by machines :-) We have guest posting enabled on our official board here as well, and as you see, we have no automated spam. This add-on also has many configuration settings which turn it into something different. For machines, a different thing is very hard if not possible to break.

Alternative to Captcha code is mentioned amongst our Custom modifications section. Most probably you can use it for your purpose; the only thing you shall remember about 3rd party solutions: miniBB team doesn't provide support for them. So if something doesn't work for our Captcha add-on, we will investigate and fix it; for 3rd party codes you should ask authors, and in most common cases, you will either don't get a reply, or it will be not sufficient.