What you describe is not full duplex. Two radios working together, taking turns (one transmitting, then one receiving, etc.) is the very definition of half duplex. And one radio in constant operation is simplex of course. Full duplex is always a situation where two radios are used in constant operation. One sending, one transmitting.
Full duplex using two radios on different frequencies is old school. Just a matter of a good combination of filters and enough frequency separation.
Full duplex using two radios on the SAME frequency, using directional signals is difficult but not undo-able. As long as you can prevent your receiver being blown up by your own transmission signal (and hope an unexpected reflective object in your signal path doesn't undo all your careful physical transmitter-receiver antenna separation).
Full duplex using two radios (both in continuous operation, one transmitting, one receiving, as defined at the top of my post) on exactly the SAME frequency while using a SINGLE (omni-directional) antenna is a true nightmare. And apparently these guys did just that with technology that promises it to be available in hand-held appliances.
RTFA, they used a combination of a circulator on silicon (which is the most innovative part. The circulator used in the project described by the article should kill most of the transmitted signal otherwise picked up directly by the receiver) and echo cancellation (which they developed earlier and is used to subtract any transmitter signal left which should mostly be echoes from objects that reflect the transmitted signal at distance and possibly internal echo from a sub-optimal antenna) on the received signal at the receiver end, so they can then try amplifying what's left. Which should be the (weak) signals that are transmitted towards the antenna by another transceiver.
Exciting stuff :)