I wanted these to be ACORN-SHAPED, but alas, neither Make Playing Cards nor The Game Crafter currently offer that particular shape. (For shame, y'all.)
Simple: coz GACHA refers to THESE things.
These ubiquitous, two-part, shatter-prone capsules that are often more expensive than the items within.
Just in case you don't know about these machines, one feeds a coin to the metal creature, and reaps the aforementioned capsule.
When I was a kid, there were several of these machines scattered throughout the hamlet of doom; most were dedicated to the display and pop-star-pushing of priceless New Kids on the Block memorabilia, which took the form of tiny buttons or stickers spouting cool-as-a-cucumber phrases like "hangin tough" and "you got it."
Anyway, a great many theorists have...theorised...that the APPEAL of such machines is the whole "will I or won't I??" aspect, aka "will my next acorn-shaped capsule deliver an item I'm MISSING, or will it be an extra back-up copy of my favourite sticker?" tempered with a healthy dose of "oh, sweet patron saint of teenybopper boy bands, I do IMPLORE and BESEECH thee to please, PLEASE, PLEASE let me get ANY button except for JON! And DANNY! And DONNIE!"
Some trading card games carry with them such an appeal, though the Sally of Today would MUCH rather just buy a case of 12 or 14 boxes and call it a day.
(Yes, that would be COMPLETE boxes, aka "have every single item in every single collection.")
Anyway, hopefully you've now gotten the picture of what these machines are, coz the rest of today's spiel won't make sense unless you know this part.
Moving on, in Japan, these machines are called GACHA, from "gacha-pon," or the sound a machine makes when one turns the handle and drops an acorn. (Allegedly. I've not yet been to Japan, tragically. But if ever I do, you can bet your sweet life that Sally's gonna be testing the veracity of this sound-effect claim.)
THAT'S why I called this game GACHABOX--because of the "which one will I get??!" aspect, but also because most of the games I've designed since, like, 2011 or so... have ended in BOX.
There's COMBOX and PROJECTBOX and the brand-new PRODUCTBOX. And DRAMABOX and... well, you get the idea.
The element of uncertainty -- "which cards will I get in this pack?" -- is also repeated in the GAME-PLAY of GACHABOX.
Well, at least TWO of the official methods of playing, anyway. (As with almost ALL Sally Bishai Games, there are more than ten different methods to play, ensuring replayability, of course, but also new lessons to be learned from each style of playing.
Anyway, there's some tropical storm thing outside, so thus endeth the lecturette about the reasons behind the NAME of this GAME.