Rime has been rated for PS4, Xbox One, Switch, and PC in Brazil and Australia
Tequila Works, for all the problems they have had with Rime, it appears that they are still pushing forward with the troubled game, and the latest update we have on it, is that it looks like Rime will be playable on every major platform. The Brazilian Advisory Ratings Board officially rated Rime and lists its platforms as PS4, Xbox One, Switch, and PC. After the reveal of the Brazilian rating, it was discovered that the game was also rated in Austrailia.
A press release that came out several months back referenced "platform availability details" that would be coming in early 2017, which pointed to the game no longer being a PS4 exclusive.
Naturally, there's still no indication of when the game is going to release, but at this point, it doesn't matter. The game's development has been so troubled and protracted, that it's just better that the game come out whenever it's fit.