I don't even think you got the right to stream any music online publicly. Even if you bought a CD or whatever.
Companies like spotify or last.fm pay fees to whichever organisation ask for it.

Now, should we care? I mean, my online radio is for me in the first place, but it happens to be available to wichever knows the address. Could I be arrested for that?

EDIT: Found this to explain radio licensing: https://radio.co/blog/do-i-need-a-licens...net-radio/