I'm a US native. I've never heard of the game. It might be outdated; it might be regional. I use it, and I've heard it used, in a joking way, simply to mean something handy. "Handy" means something that's useful and often needed, so it is kept nearby, "at hand." "Dandy" is an outdated expression for something very good. So "Handy-dandy" is an intensification, and it's fun to say because it rhymes. It is a little hard to describe this kind of humor. It could be called "droll" or "whimsical." It consists of intentionally using an outdated expression, a "corny, old" expression. It could be just for fun, just to express personality, just to be different, or just to show that you're only half-serious. For example, "We can use Excel's handy-dandy 'Analysis Toolpak.'" It is as if this calculation tool were like a can-opener in a kitchen drawer. Here are some other examples of using intentionally outdated or rustic expressions as whimsical humor. "It's 10 pm, it's getting late--I'd better skedaddle." ("Skedaddle" is outdated). "Fair maid, would'st thou go with me to yon Dunkin' Donuts to quaff a flagon of coffee?" (This is an imitation of the language you hear in books or movies about the days of King Arthur). "But Lewis is a vegan. So, the sixty-four-thousand-dollar question is: does the Longhorn Steakhouse have vegan entrees?" ("The Sixty-Four Thousand Dollar Question" was a TV quiz show with a $64,000 prize.)

I think it is just an antiquated way of saying that something is very useful. It is the kind of thing my aged mother from the Midwest USA might say. You wouldn't hear it too often these days.

I have never heard of it.