To let the Chinese know that they should not consider violating Japanese air space, and punctuating that point.
Interestingly, China has sent in unarmed Y-12 prop planes (small, pathetic things, basically cessnas) that have intruded into diaoyu/senkaku airspace, yet the Japanese never mentioned anything about shooting down those before...
I think this Japanese move regarding UAVs have two motivations:
1: The japanese (and the rest of the world) were caught a little off guard when the PLA sent a BZK-005 on such a relatively distant patrol.
2: The japanese are naturally a bit more wary regarding a BZK-005 entering their airspace than a Y-12 (although technically both are unarmed and all BZK-005 offers beyond Y-12 is a more potent FLIR and electronics suite), as it is a "military" aircraft
3: The BZK-005 of course is unmanned, meaning it cannot respond to hails from intercepting fighters as a manned aircraft can. However the JSDF probably calculate that they would have far less to lose if they were shooting down an unmanned military drone compared to a manned, and relatively benign looking Y-12 (the latter of which has actually entered "japanese" air space)
If JSDF says they'll start shooting down manned aircraft too, that's when you know things are getting real.