The link you posted is not the same. It’s only for video, not audio.
You haven’t clearly answered how do you connect your audio, hardware-wise. Do you connect some cable somewhere and where?
I am surprised you are saying that audio is working in Windows. How? The internal audio is broken. If you don’t use the USB audio, then how do you connect audio output to the speakers? Show us a photo.
Please, verify that audio HDMI is working in Windows and this is all a misunderstanding.
PS.: I have used this kind of adapter. Not all of them provide audio and not all of which provide audio do it right. The specific specifications hw is much more expensive than most similar adapters.