There certainly IS xp, and levels, and you have 4 skills to put the points you get for levelling into. Which affect how much benefit you get from matching that colour's blocks. So I dont know where the reviewer gets the idea there is none.
There are no classes as such. But that is neither good nor bad from a design perspective. Classes are somewhat limited in that they rigidly lock you into a pre-set path. In the original Puzzle Quest you effectively had little choice in the matter of char advancement. Pick a wizard, you had to put your points into red/destruction. It was very linear, and you only had a set number of strategies. As you levelled up, you replaced one power with the more powerful version.
In Galactrix your ship is the avatar. It can be small, large, big cargo hold, fast, bigger shields (which you have to get through before doing damage to the ship itself) have more equipment slots and so on. You can have 3 ships with different loadouts, as well as carrying around numerous extra equipment to slot into your best ship if you hit a tough battle. (Coming up against one of the factions that relies on its shields, anything that helps disable them is good)
Since you have total control on what skills and abilities your ship has, having a 'class' dictate your play-style accordingly would be stifling and require any sort of strategy on the game's end to be geared towards that class. Or you just couldn't complete the game. It would end up getting repetitive once you hit a certain plateau of skills. (As it did with any class in the original Puzzle Quest) Here you have lots of variations to choose from to suit your personal play style. This is not necessarily 'better'. It is however different to the original.
Multiplayer 'class' based games almost always end up as glorified rock paper scissors. With move and counter-move all set and known in advance. Coming up against a Red-based char? You better be the counter-class or its goodnight. And so on. Here strategy (in the form of what you equip your ship with) and tactics actually have meaning. In the single player game, you have to think about your ship & skill loadout before entering the fight. And if its too hard, you can swap some skills around, try a different ship etc. Whereas before you had to go away and level your char before brute forcing your way through it.
There are some annoyances with hacking the gates its true. It does get old a bit fast, especially since they are timed, and you might start an unlucky chain with 10 seconds to go, and only one colour to unlock...and bang time out. A simple clock-pause on any chain over 2 would solve this.
But otherwise its a very solid and engaging game.