The stream goes out over the internet....and your computers picked it up at different times. Its not like an over the air signal where any radio will play at the same time.
Its not perfect by any means, and internet won't "replace" radio over the air, its either an enhancement to allow to listen to some stations that you don't get all the time (like me with CKLW, can't get it at night where I live) or the chance to listen to some far away land, like Australia, or England, the other night I had a great time listening in on Christchurch, New Zealand. Also, only in rare cases do you get EXACTLY the same thing as the over the air station. Commercials have to be blacked out in many cases and pro/college sports can't always be sent down the stream either. Still...it can be a lot of fun. The key in my opinion is making it as close to radio as you can. You can use your computer speakers or buy a transmitter and send it to any radio in your house. I know you don't have a smart phone TT, but a Smartphone on the go, plugged into your car stereo is very cool. Internet radio/TV is something that can be a great enhancement. Heck, I'm enjoying a hockey game as I type this:
http://freeredwings.tv/
"Those who want the Government to regulate matters of the mind and spirit are like men who are so afraid of being murdered that they commit suicide to avoid assassination." -President Harry S. Truman.