I don't know about https specifically but winamp could handle all kinds of streams.

Looks like curl and opus want it https://github.com/search?q=repo%3AWinampDesktop%2Fwinamp+openssl+language%3AC&type=code

Three streaming (like pointed in the other comment) was my initial reaction too, but indeed at the time https for streaming would be very rare.

Another possibility is to realize that openssl isn't just for communication, but also has implementation of cryptographic algorithms.

Perhaps openssl was used for validation of licensing key? For example they could sign the license with their private key and WinAmp could verify it's authenticity with its public key.

Maybe to connect to their update servers and validate updated binaries or something like that? Not sure if it supported calling home to get updates.

Couldn’t you look at the code and see what ssl calls it’s making?

i remember listening to icecast radio on winamp back in the day