If a radio station's transmitter fails temporarily, does their web stream stop being "radio" temporarily? What if the transmitter fails and never gets fixed? What if the transmitter only covers a very small area, like a single town, or a single college, or a single block? How many feet of coverage are needed for it to be "radio"?

Would it still be "radio" if the station's transmitter were changed to an open wifi access point that broadcast the stream? Or is AM/FM modulation necessary for it to be "radio" -- and then what about satellite radio?

Seems like a really silly set of questions to quibble over. Better to say that technology is complex, ever-changing, and ofen broken, and that language is complex, ever-changing, and generally imprecise. Any mapping between technology and language will thus be imperfect.

Instead, we could consider that traditional radio broadcasts as a medium of expression afford a certian collection of behaviors, and that other things close to them in the continuum tend to fall under the "radio" term at the moment.

(Notice that cable TV is still considered "television" despite having abandoned atomspheric transmission decades ago, and more recently moving to TCP/IP, and indeed often not being watched on a television.)