While you can enjoy the basic game on it's own, you'll need to play the rhythm portion as well to rack up high scores earning stars to unlock new song sets and powerups. Dropping blocks on the right beat will start filling up a multiplier meter. Dropping on not on the right beat clears the meter and multiplier, but letting blocks settle on their own preserves any multiplier and progress. Powerups (such as bombs and scoring bonuses) are only primed if dropped on rhythm and later cleared. Finally there are "Super Beats", which temporarily double the multiplier if hit.
On the "Casual" level, I found the gameplay combination relaxing and interesting. Songs last about four minutes and tend to have plenty of beats, which makes for a pretty satisfying way to fill time once in a while. With playtime limited by the length of the song, it's fairly easy to get the satisfaction of beating each stage. The "Experienced" level ramps up the challenge by raising the score to earn stars introducing four-block squares and making the pieces fall faster. What tends to happen for me is either A) I focus on the match-three game and don't score enough points to earn stars or B) fail out of the song by dropping pieces before they are set to make combinations. In other words, when the game falls apart, it splits exactly on genre lines.
I can't help but be reminded of my initial experience with Tetris. On the surface, Tetris rewards neatly packed tetrominos and clearing lines as quickly as possible. But as you clear levels the pieces fall faster and faster until it's literally impossible to move pieces into place before they hit the stack. No matter how good you are, the game cannot be beaten. So you need to adjust to the goal of getting a high score, which rewards actions like hard-dropping pieces and clearing four lines at once (getting a "Tetris"). To me, building in such a way that deep pits form in order to drop an I tetromino appeared the antithesis of packing pieces properly. For years I gave up my Tetris addiction rather than change my play style. Playing the more advanced levels of Groovin' Blocks requires an equivalent paradigm shift. In this case, you must drop blocks more or less randomly on beat to build a multiplier and then capitalize on it by clearing blocks more or less methodically.
If you like 8-bit or electronica music, the set list is solid but short. After beating my head against particular songs, my enjoyment of the music started to drop off. Now that I've breezed through the lowest level, I'm stuck on the first set of songs in the middle level. Unlike most puzzle game that can be muted, in Groovin' Blocks you are competing against the music to pass a particular level. Turning off the sound deprives you of a key clue toward getting a high score. On the other hand, the visuals provide enough cues (rolling beat bar and pieces flash to the rhythm) that playing muted is (barely) possible. Also deserving mention (and commendation) are the calibration and colorblind options, which ought to be standard for rhythm games, but aren't.
I should point out that I was given the game code via the developer, Empty Clip Studios. There's very little chance I'd have bought it with my own money and I don't think I'd recommend anyone else paying for it unless they absolutely love the soundtrack (which can be sampled via Google). If you think you can handle hearing these tracks as many times as it takes to crack the scoring goals needed to move forward, then I'd recommend the game to you. (I should add that I did not try the multiplayer mode, but it seems unlikely to have potential to sway my opinion.)