Interscatter technology
No, to use existing available radios, you need two devices.

Backscatter communication is a standard thing, used by all sorts of RFID tags for example. Radar is also a form of backscatter. This can certainly be done with one antenna, one device, though they sometimes use two, for the same reasons as below.

The way that the interscatter signal is generated, it is created from the Bluetooth signal, at the same time. What is so clever about this method is that it uses unmodified Bluetooth and WiFi devices.

A smartphone cannot simultaneously transmit a Bluetooth packet and receive a wifi one. Phones often use a single chip to do both, and the signals share a single antenna. This works well enough for simultaneous Bluetooth and WiFi, because the packets are short and there's enough time to switch between the modes.

The reason they're drawing a separate transmitter and receiver is that the receiver needs some physical separation from the transmitter. At the receiver location, the scattered signal will be much weaker than the original Bluetooth signal, perhaps 30 or 40 dB. Although it's on a slightly different frequency, the receiver will struggle to separate the two. But at the transmitter antenna port, the scattered signal will be more like 100 dB weaker, than the Bluetooth signal, making it impossible to separate without special hardware filters. This defeats the main feature of the method, using existing radios.