QFN-like package identification
On your pic of the "chip" there are traces visible on the bottom of the package. I would say that this is not a "chip" but rather a small piece of PCB with components mounted on it, then probably hidden under epoxy. PCB material can be standard or custom.

So, this would be a hybrid circuit perhaps, there is no way to know unless you want to pop the cap off it. While it looks like a QFN, it seems to be a totally custom device.

If you want to make a breakout board, you will have to replicate the footprint on the existing PCB. I guess a QFN footprint generator wizard could work, but pay attention to the five pads in the center which seem to correspond to five solder balls under the "chip". These must be connected to something, possibly to get rid of heat... make sure you don't forget them.

Soldering this will require hot air or an oven...