The markings look like an Atmel part (it starts with "AT", which is common for Atmel parts). Given the size of the chip and context which you provided, I figured it was probably a serial EEPROM. Looking through Atmel's serial EEPROM datahsheets, your mystery chip is almost certainly an Atmel AT25128B-SSHL SPI EEPROM, which matches your chip's product ...
My guess is that the protocol is standard, using a non standard protocol between two devices involves using bitbanging which is not very useful.
Let's assume then that the protocol is standard.
It's not SPI, SPI needs 4 lines To work. I2C needs two, RS232 needs only two.
I don't know what the third line job is, maybe it's used for trigerring/synchronization ...
You can try this:-
All Data Sheet
(sorry this won't allow me to post more than 2 links, you can refer wikia page for other sites like All Data Sheet)
Identifying and deciphering the part number Deciphering a chip's part
number is a very ambitious process and most of the time, typing the
whole part number in a search engine gets you nowhere.
It may be possible. Based on the data sheet you posted, you need to see if Pin 9 is tied directly to ground, or can be controlled by the CPU. If it can be controlled, the chip can be re-programmed.
If Pin 9 is tied to the CPU, you may then be in the realm of trial-and-error to see how to control that pin.