Hi,
I don't see what's the problem with the way it is now.
When the customer will click on the download link, the file will be downloaded by his browser, and it will ask the customer if he wants to open the file and with which software. If he chooses his media player (or his PDF viewer), the music will play (or the PDF will be displayed). That will work by default on any smartphone or computer.
On top of that, the file will be on his computer and he will be able to copy it to another device, and play it again easily without having to download it again.
So it looks much practical to me than having a player on your website to play the file from your website.
But well, to answer your question, there is no integrated player in HikaShop file product files. If you want to add one, you'll have to edit the file "downloads" of the view "user" via the menu Display>Views and modify the code displaying the link for the download of the file, to display instead your player or a link to it.