It sounds to me like the intention is to stream over the local LAN, not over the internet. As long as the streaming port is blocked to the outside world at the modem, I don't see how that's any more illegal than playing your music collection or audio from a SeriusXM receiver over a Part 15 FM station or a bluetooth device within the confines of one's own home or car.
I don't think anyone has ever been arrested for broadcasting Howard Stern over FM to surrounding cars, and that's been happening for years. Ancient Modulation "phono oscillators" go back even further, to the 1940s at least. As long as the intent is not to broadcast to the general public, I don't think there are any legal or copyright issues. I think that's considered "fair use" of copyrighted material, so long as it's for personal/family use only.