The story behind the conception of the original Puyo Puyo continues to be told, retold and disputed to this very day, with ex-Compile folk coming out of the woodwork every other month to poke holes in the accounts of Compile's former president, so I'll give you the tl;dr as best I understand it:
- Tetris blows up; Compile's president orders a small team to devise their own falling-block game
- this team pokes around with a domino-themed game for quite a while, but it goes nowhere
- an informal meeting is held to course-correct the game; they basically decide to dump the game onto young planner Kazunari Yonemitsu, who tagged along to the meeting for the hell of it
- in order to assuage the burned-out programmer who was sick of working on the game and didn't want to return to a flailing project on top of their other work, Yonemitsu proposed tying the game to Madou Monogatari, with the implication that they could reuse existing assets and therefore not have to spend a lot of time on it
- due to concerns about the game's similarities to Dr. Mario and fears that Nintendo might see the game as Compile cloning their ideas for other hardware, Compile's president negotiates a simultaneous Famicom Disk System release, published as a cover disk for a certain Famicom magazine
- the game gains enough critical praise that the president decides to push for an arcade release and cashes in some favours from Sega to make it happen; Sega throws their weight behind it, as well as some design ideas, and the rest is history
The president has spread and continues to spread all sorts of grand claims about the motivations behind the Madou Monogatari theming—claims that the devs were otaku types obsessed with what would now be called "moe", or that they had big visions for the future of character-based puzzle games, etc—that the actual devs have strenuously denied, but most of them seem willing to rationalise these tales as simply being sexier for TV or whatever. Yonemitsu's reached the point where they simply link to their own paywalled rundown on note whenever the former president pops up in the media, and it seems that they're content to earn some lunch money every now and again and don't necessarily hold much of a grudge.
As for the game itself, it's about as raw as you might expect: there are endless, 2P vs. and mission modes but no vs. CPU option whatsoever, and the character elements, ie the occasional Arle drawing, are restricted to the title/ending screens and are absent during the game itself (and even those are absent from the FC version, iirc). Mechanically, there's a hard garbage cap and no on-screen garbage indicator, and the randomiser kinda just does whatever it wants, including in the mission mode; it also uses six colors, which was cut back to five for subsequent games. The ending is certainly worth a look, but the game itself doesn't have much left to offer.
(After the arcade version blew up, Compile converted the FCDS version to ROM for a cartridge release, and that version did change a few things to conform to the specs of the arcade game, like fixes to the randomiser, the ability to lift the garbage cap, etc.)
A little trivia on the alt-tiles that replace the puyo with little humanoid characters: Yonemitsu had originally planned to theme the game around world harmony, with characters linking hands in an expression of unity, until the programmer pointed out that only being able to match people of the same colour undercut his message, so he pivoted to puyo.
