Perhaps I'm missing something but if I have Skype why is game or party chat important?
Do you have Skype on 360? Didn't think so. And don't even say that you have it on another platform because there is no way to connect your 360 friends to your Skype contacts. The whole point you're missing is not a big deal for Xbox One users. It's that 360 users have no way to connect to XB1 users other than seeing them on a friends list. They can't chat via game or party chat. Maybe private chat or even private messages(voice or text) will be supported, but they haven't said either way.
Tommy McClain