Everybody has an ADIZ in the area, just that China is the last to declare one.
Most comments I see on the web, there seems to be a mis-understanding between an No Fly Zone (NFZ) vs a Air Defence ID Zone (ADIZ).
The purpose of ADIZ is for identification. If the planes don't ID themselves, then other measures are to be considered.
China doesn't have to respond to every blip on the radar that crosses the boundary and maintains radio silence. They reserves the right to.
ADIZ is a concept. If for most part, planes (mostly civilian) start to ID themselves (and they will), then the concept holds true regardless of whether they are recognized by other governments or not.
A lot of media (whether on purpose or not), calling it an Air Defence Zone (leaving out the ID part) creates a very misleading impression.
The ADIZ is one thing. The other more interesting point is the inclusion of the diaoyudao/senkaku islands into the zone.