The narrative alone is enough to sell the concept of this game. It provides a very clear picture of what the player is supposed to be doing, letting them quickly figure out how the gameplay is supposed to go after a couple launches. The gridless, "Tetris"-style of building was a bold choice since it lets the player make some unconventional rocket shapes, although trying to fine-tune the piece-slotting can be a bit frustrating since the pieces move a bit too quickly and seem to automatically detach from the player's control the moment they touch another piece. It might have been better to allow players to continue moving/rotating the pieces up until the center of their base (so not the corners) makes contact.
Shortening the time it takes to weld pieces together would also make building a lot more easier, and less likely to fall apart due to sliding across angled pieces (whether intentional or not).
I do like that the game actually expects the player to discard pieces that won't be good for the rocket (I thought it was a "cheat" until I saw the teasers after playing), although this does create a situation where the player will favor straight, tall pieces over the "S" or "T" shaped pieces.
I originally kept playing under the belief that having a "thick" rocket (i.e. a width equal to the base) would give me more fuel to use for liftoff, but the ratio of thruster-to-piece weight kept making this fail. It might be good to add a display showing the rocket's current "weight" relative to thruster count so that the player can tell when their rocket is becoming too heavy.