Probably the most major factor is that the computer speakers and associated amplification are being asked to produce far less volume than the speakers in your main system. If you were to put the computer system in your main listening space, set up its speakers on stands, and turn up the volume to produce realistic volume levels at your listening position, the sound card would undoubtedly be driven into extreme clipping, and the speakers would most likely be destroyed if your ears could tolerate the distorted sound for more than a few seconds or minutes.
Another factor that helps is that the internet radio may consist of the same heavily compressed audio that is typically sent out over the airwaves. The compressed dynamic range causes you to reduce the volume level, making life easier for the amp and speakers.
And of course the computer speakers don't have any deep bass, which is a major cost driver in a quality system.
Another factor is that the speakers, sound card, and heavily processed source material probably homogenize the sound, making mediocre source material sound more pleasant than it would on a high quality, more revealing system, but sacrificing the ability to make high quality material sound as good as it should.
Best regards,
-- Al