How to detect a Bluetooth low energy device or IBeacon without a smart phone?
The majority of BLE chipsets can function in the central (detector) role as well as the peripheral one.  A noted exception however is the NRF8001 used on some Arduino BLE shields, which cannot be a central (detector) - but something based on an NRF51822 or CC254x with the right firmware could.  

The module you link is plain bluetooth, not BLE at all.  

Finally, an embedded board which can host a USB BLE adapter can probably detect advertising transmissions - there is coverage on StackOveflow for doing this with a raspberry pi, but in a way that is portable to most embedded Linuxes.