As you are adding hyperlink in the excel, that logically means referring to a file in a specified location hence when you click on the icon that navigates to that file and it opens in a new window as it an audio file.
For playing in the same screen in a html page we need to have the
I tried the VBA script that was playing the audio but while we convert the Excel to HHTML file, that VBA does not work as that VBA is a feature of excel file, even you might have seen that popup that some features might be lost if you save Excel as .htm. So I think it will not be possible to have that on the same page as long as we convert it from excel OR may be more R&D is required. Good luck!
Below are the references I used: