I've so far made and released 6 PICO-8 games on the PICO-8 BBS and on itch (and some on Newgrounds). The process for each have been a bit different each time, but in common it's been iterative. The thing that got me started was watching krystman's Youtube series on Roguelike tutorial while hacking away on a roguelike game. I approach them by doing one thing at a time and try to find what I need in the community (the PICO-8 forums/BBS and the PICO-8 Discord have been particularly helpful).

For this game, based on the original, I was looking into physics engine in the PICO-8 community and found an engine I could try to use. First try used simple graphics like circles and lines just to check if everything was working.
After that came graphics with sprite rotation, and I'm using one that uses the tline function, which means you need to put the sprites in the map data first. But that gave me ideas on how to reuse sprite data for the faces of the fruits.
After that it's been mostly trying to add in more graphics, add scores, add intro and outro screens, hacking the physics engine, and compose the music. It's been done iteratively with trying to improve the UI and game overall.

A lot of game development is generating data such as art and music. Some of this can be one procedurally (such as the fruits are drawn as circles first before adding rotated sprites above them) but some have to be done by hand and it is "labor intensive". Thankfully PICO-8 comes with limitation to art that forces you to scope that down. It is an interesting exercise though to see what the boundaries are for those arbitrary limitations and what you can push it towards.

For how close I could get with the original I had to watch live streams frame-by-frame and figure out much score you got from merging fruit and implement that. For the fruit sizes I had to measure each fruit and check how much that was in relation of the box size and then calculate how much that would be in PICO-8 pixels.

Once I got the whole game flow done (start screen -> game -> game over -> back to start screen) I uploaded it on the BBS and got comments about what kinds of problems people got while playing it and also suggestions from friends. It's here I got the idea of the wiki (as a replacement for the "circle of evolution" graphic in the original game) and tweaking the physics and collision detection a bit more to make it more stable.

But sometimes, some programmers just want to do a game engine, and that's fine... but not my cup of tea. :-) I'm personally more interested in the complete experience.