I recently took apart an Entex Pacman2 which I still have from my childhood.

I found this strange CPU in it (and not much else): Hitachi HD388A20.

It belongs to a family of 4 bit processors (HMSC40) with 10 bit words and 10-12 address lines (512 bytes to 4KB). It's a weird little thing. You can still find the manuals online. They have pins that drive the display directly and some addresses are for storing bit patterns which you can move directly to the display. I guess many portable games from the 80s must have used these chips, but I had never heard of it.