I'm curious, why does this require OpenSSL in order to compile? I'm not aware of any audio formats that use encryption, but I could be wrong.
My first thought was for connecting to https streams, but I don't remember Winamp having this capability. "Back in the day," I used Winamp for playing local audio and RealPlayer for what little streaming was available.
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.