I use MPlayer pretty much all day, every day to play internet streams. Not sure exactly what the error means, but it could be that the link is actually to a playlist, rather than actually the MP3 stream.
I listen to a lot of sub.fm, and with their sources MPlayer needs the right options. Generally they have a playlist file (a plain text file) for compatibility with VLC, iTunes, Winamp etc., which details the actual audio stream. SubFM also have an embedded player on their website, these days (I think) is basically HTML5's <audio> pointed at the same stream as that in the playlist.
They make it pretty easy to tell from the URLs which is a playlist and which is the stream
I use a wrapper on MPlayer to build a command that is reasonable for my use. Try these two, and they should work.
mplayer -cache 384 -msglevel cache=-1:identify=3:statusline=-1 -ao alsa:noblock -playlist http://www.sub.fm/listen.pls
mplayer -cache 384 -msglevel cache=-1:identify=3:statusline=-1 -ao alsa:noblock http://stream.sub.fm:8050/SubFM
If not, try outputing the audio to nowhere, just drop it with the right options, and that will say if the problem is with the audio out of MPlayer or it taking data in. If you have MPG123 installed it should work, here on my Slackware laptop that is the decoder used if I don't specify any other.
Have a look at mplayer's manpage, you can turn messages up more and more until it starts saying something that might be a bit more illuminating.
Shoutcast servers also seem to do some slight user-agent trickery. Hit a shoutcast server with a client that identifies as Mozilla* (ie normal web browsers) and the server gives an HTML status page. But hit that same server with a music player and the server gives MP3 data. This behaviour mostly means a shoutcast server can be recorded just by pointing wget at the stream.
I am a bit thrown by you saying MPlayer on Windows 10 starts at a random point. A stream off the internet is generally like an FM radio, it playing starts with whatever was going out at the exact time the radio is turned on/the software run. I hope I am not patronising you there....
A caveat though is that if you point MPlayer at an MP3 file sitting on a normal web server: what might be seen as a download can be "streamed" with the right software. For example, Sub FM have an archive of shows. You can download past shows to a file on your computer, or just give a URL to MPlayer and it will download the data, play it as audio, and throw the data away, it streams it.
"Stream" can be a synonym for broadcast, but really it is just a form of downloading. But the media industry hate the word download, so use stream to also mean other than broadcast. eg Netflix, where the user actually downloads and the (DRM'd up) software throws the data away after displaying it.