The screens made it look like just a Columns clone, but that bit about rhythm makes me wonder just what's going on.

Yeah, I'm curious... what does a block-rhythm game play like?

Okay, so basically it's a lot like Lumines.  Surprisingly awesome music.  You know how most Tetris games and clones let you press down to instantly drop a block?  In Groovin' Blocks, you try to drop blocks to the beat of the music.  Doing so builds up a score multiplier and activates power-up blocks.  The different power-ups are unlocked (and leveled up!) as you play.  The first difficulty tier has nine songs; I'm not yet sure if there are other songs locked up in the higher difficulties, but it seems likely given the structure of the game.

Warning: it's 316 blocks to download.  But so far, seems like a bargain at only 800 points.

By the way, there are no motion controls.  You can play with the Remote held sideways or with the Classic Controller.

That's an interesting comparison to Lumines, how do you exactly eliminate the blocks? Is the elimination based on colors of the blocks like puyo pop, or is it strictly based on the rhythm of the songs?

You eliminate blocks by matching at least three of the same color, horizontally or vertically.  Once you make a match, the block removal is "contagious", meaning that any adjacent blocks of the same color (but not part of the match) will also disappear.  It's also quite similar to Meteos, now that I think about it, except you can't shuffle around blocks that have already been placed.

I'll stay away, I have no sense of rythm. Or at least no sense for rythms dictated by outside sources.