Fun game, I'm a sucker for Tetris Attack style games, so this was right up my alley.
Linking the matching game to the various ship systems is an interesting choice. It adds an extra layer of strategy to a standard tile matching mechanic, but I wonder if some different tile images would help decipher things at a glance more easily. Like weapons could be a little missile, and shields could be a little semi-transparent circle, and speed could be green chevrons like >>>, etc... Then the player wouldn't need to refer back to the 'key' as often to make choices.
Also, I found myself focusing in so much on the matching, that I couldn't watch the action with the ships in the top section. Not sure how to address that though, I probably just need to git gud.
There's a lot of promise in this if it gets some further polish and enhancements. Great work!