The game's developer, Spanish studio Tequila Works, came under fire for the difference in pricing. Its follow-up comment to Eurogamer didn't help matters much, either.
Since then, we've done a bit of digging, and it turns out more expensive Nintendo Switch games may not be entirely the fault of developers.
Publishers and developers are free to set the price of their Nintendo Switch games, as Nintendo of America boss Reggie Fils-Aimé has already said, but based on conversations we've had with developers this week, it looks like companies making multiplatform games that are also coming out on Nintendo Switch are stuck between a rock and a hard place.
Let's start with Tequila Works' initial comment on the Rime situation:
"We set prices for our products based on the costs of development and publishing for each specific platform."
What does this mean? Well, we've heard that the cost of manufacturing a Nintendo Switch game is higher than the cost of making a PS4, PC or Xbox One game, because the cartridges the Switch uses cost more to make than Blu-ray discs.
We've also heard that the cost of the cart depends on the size of the cart. Switch game card carts come in a variety of capacities: 1GB, 2GB, 4GB, 8GB, 16GB and 32GB. At a high level, the bigger the cart the more expensive it is, although the price may vary according to print run (lower the volume, higher the price, for example - an issue that may affect indie developers who don't expect to shift a huge number of copies of their game).
Developers working on Switch have to be mindful of the size of the game, because that will determine the cart it'll ship on. (As an aside, we asked Tequila Works how big Rime is on Switch. It replied: "as the Switch version is still being developed by Tantalus Media, we cannot estimate the final size yet.")
But why would a Nintendo Switch game cost more on the Nintendo eShop? Digital games, after all, are just a download. There's no need to factor in costly cart manufacture with an eShop game. Well, we've heard that Nintendo's policy is that Switch eShop games should cost the same as their physical versions, in a bid to keep bricks and mortar shops on-side. A shop such as GAME, for example, is unlikely to go all in on a Switch game if you can download it for half the price instead.
So, we end up in a situation such as Rime, where the game costs £39.99 on Nintendo Switch physical and digital, when the PC, PS4 and Xbox One versions cost just £29.99 physical and digital.
Rime isn't the only game to suffer from this problem, by the way. Puyo Puyo Tetris, from publisher Koch, costs £34.99 on Nintendo Switch both physically and digitally. It costs £24.99 on PS4.
We've heard this policy is why some smaller publishers and developers are going with the eShop only for their Nintendo Switch games. To release a physical version would mean factoring in the cost of manufacturing a cart, bumping up the price accordingly then price-matching the digital version.
Snake Pass, from Sumo Digital, comes out on 29th March priced £15.99 on all platforms: that's PS4, Xbox One, PC and Nintendo Switch. It's digital-only. There's no Switch cart.
"Snake Pass is digital only," Sumo COO Paul Porter told Eurogamer, "and we have no issue keeping the price the same across all platforms digitally. Indeed, it was important to us that people wouldn't be penalised by which platform they decided to purchase."
For Nintendo, it's not a good look. Here we have a new console from a company already accused of ripping off its customers with higher-than expected pricing. For many, the Switch itself is too expensive at £280. Mario Kart 8's port, which adds little, is £50. Then you've got the new Zelda, whose RRP is £60. Super Bomberman R costs £50, too. (Nintendo declined to comment on this story.)
So, back to poor old Rime. We went back to Tequila Works to try and find out more about the game's pricing, and received the following response.
"We cannot enter in any specifics, but we can assure you Rime's price is based on the costs of development and costs of manufacturing for each specific platform."
Hopefully now you know a little bit more about what that means.
Additional reporting by Tom Phillips.