The pin header doesn't look that small?
The device is a module, don't worry about the chipset, it's a CSR chipset alright, but it's pre-installed on a module, are there any identifiers on the module?
Look for a BT LE module on ebay and I expect you will find it.
I expect the 328 runs a arduino sketch which talks to the BT unit over AT commands or HCI, or something else, and then modulates an IR signal out of the IR LED
It looks to essentially be a BT LE to IR translator