It's actually on 4 different consoles (5 counting Wii U)
The first Rhythm Heaven we got in the Americas/everywhere outside of Japan was just called Rhythm Heaven (Rhythm Paradise if you're in the UK) and that was on the DS.
The second one we got is what the video is based off of, Rhythm Heaven Fever. This one was for the Wii, but you can currently pick it up for your Wii U on the Nintendo eShop.
The third game we got (and most recent) was Rhythm Heaven Megamix. This was on the 3DS and features games from both previous titles, some new ones, and a few games that originally were Japan exclusive on the Game Boy Advance.
Hope that helps clear things up!