Further to my dump a couple of days ago of one of the as-of-yet totally undetermined 1.8in handhelds, I decided to dump another slightly older one, a 106 in 1 I bought from Taobao a few years ago, model number "8533" and PCB date 2013-10-18. You can find the ROM dump here:
http://davidstech.net/games/multis/106%20in%201%201.8in%20DigitalPocket%20Handheld%208533.7zThis time, there are at least some strings in the ROM. At 0x2129 there are the names of all the games, separated by 0xFF. Elsewhere there is other in-game text and also a reference to a hardware test and a checksum.
More interesting there is what is very clearly valid 6502 machine code at various locations in the ROM, the first example I noticed was at offset 0x40436 immediately after the text NS-TOWER and its 0xFF "terminator". This does seem to narrow down the possibilities for what it could be, and also suggests the possibility that it's architecture is somehow derived from the NES. However, I can't immediately find any particularly NES-esque code like writes to the PPU register space. Hence I think it also possible for it to be GameKing derived, as that also had a 6502 based processor.
I can't find obvious assembly in last week's 116in1 ROM dump but given the lack of strings in that dump I think it may be scrambled in some way, which I will investigate further.I'm going to try and do a bit more research and experimentation, maybe one day we'll have some kind of emulator for these devices.
Well, that was easy, I don't even know why they bothered. The 116in1 dump I last week made was scrambled with the world's best encryption system - XORing with 0xE4... Now strings and assembly are visible and it looks structurally similar to the 106in1, also the name "tony" appears early on - if Tony is reading this, please reply

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Here's a descrambled version of last week's dump:
http://davidstech.net/games/multis/116%20in%201%201.8in%20Retro%20Pocket%20Games%20(descrambled).7z
A bit more investigation and it appears the code is for the 65C02, not the plain 6502. I can't find anything that points to a particular platform; my best guess now is some generic 65C02 based microcontroller that either has enough RAM that the bootloader copies code from the external SPI flash to RAM, or that supports directly running code off SPI flash.
The LCD display appears to be a generic "microprocessor parallel" type interface so the processor wouldn't necessarily need to have a PPU or display interface if that was done in software. It also seems that the processor might have a speaker driver built in which would narrow the search further.