Reading all I can say this your problem is that you're assuming similar machines are also similar in how they manage sound internally.
This isn't true. Different computers can have different sound chips. And different sound chips have different ways of separating sound to different outputs. Also, you might have set up things differently in both machines.
From experience, you can check your machine's documentation and check if there exists any option inside the BIOS that enables that physical separation. As this is coupled with how the sound drivers work, there can also be something in the sound driver's documentation about it.
Ultimately, you might have the bad luck that there is no redirection (i.e. the sound signal is simply passed to both output devices at once). This last one seems less likely, as it can be perfectly conceived that one would use a better pair of headphones rather that the usual inbuilt speakers.
(I'll search a little more but since there exists a plethora of drivers and chips, I can't test accordingly)