update iTunes library from Snow Leopard to El Capitan

Hello everyone

I have a new iMac running El Capitan (iTunes 12.3) on which I would like to update an iTunes library from my old Mac that ran Snow leopard. (Don't know that number of that old iTunes because the old Mac crashed) I have copied the old iTunes folder from a backup to the new Mac. Here's what its structure looks like:

However, when I point the new iTunes to this folder, it isn't recognized and updated so I have everything in my new iTunes. I could import all the media from the iTunes Music folder but then I don't have my playlists.

What's the right way to access the old library on the new Mac?

Thanks for help!