I was involved with hardware remakes / clones of a few machines and we did reverse engineer one G&W game; I think it was Green House, if I remember well.
The games are build around a custom ASIC and the rest of the circuitry is essentially support for it.
As a side note, if you've ever opened a G&W game double screen game, you'll have noticed that the main chip is sitting 45° from the main board and this was done because at the time the boards were soldered through a wave soldering machine and it allows all the pins to be properly soldered without bridges between them.
Let me tell you how they work but be prepared that it will totally kill the magic:
The whole game is essentially a polynomial generator and a few shift registers.
The polynomial unit will generate the same bit stream every single time it is started.
Its output is fed to a de-multiplexer and each output feeds a shift register. Each bit in these registers is tied to an element in the LCD.
All motion done by the player is also mapped in a shift register and then a simple hardwired AND determines collisions. Possible actions in a given state are encoded in a matrix and the logic can swap bits at specific positions.
The game gets faster and faster by just changing the clock (which is essentially gated by another shift register).
Now with this information in mind, play the games again and you'll be able to see the logic at work where the player is essentially always on a long bit string and that when the objects become faster, so does the player input, etc.
We didn't reverse other games, but I see no reason why they'd have a different hardware since only one small matrix on top of that system can make a different game; Zelda is different, but it came years after the rest and I have no clue how it is made.
There is a bit more logic to it, but that's essentially it; some of the logic is to drive the screen; I don't remember the reason but I was explained that LCD screens from that era needed the segments to be toggled on / off to prevent some damage, apparently it's the same in watches; if anyone worked with that technology, I'd be happy to understand the details.
The hardware is tiny and could be re-implemented in a FPGA in an afternoon, but it was really clever since there is no CPU involved; It would be trivial to recreate the ASIC in software as well with very little code where each game is a different table.