The GPS only version can use WiFi when you are at home or logged into a WiFi LAN. If you are not connected to WiFi, then you need your paired iPhone for Internet connections.
If you have one of these methods of Internet access, then you can stream music to your Apple Watch.
However, say you are at work, and you manage to connect to the company WiFi network, that does not mean the company's firewall will allow you to stream music, so just because you are logged into a WiFi network, does not mean your WiFi service will be accessible over that WiFi network.
But if you are someone that has their iPhone glued to their hip, then you will almost always have internet access. Then again, if your iPhone is glued to your hip, you can stream music to your iPhone and pair your Bluetooth headphones to your iPhone, where you have a larger battery and will be able to stream music longer on a single charge.