Espalion (PC)

Espalion is a shooting game made in 2004 by a Japanese indie developer named Team DRYUAS, and as far as I'm aware, it's their only work.
It feels really different to most shooting games, and though at first I couldn't put my finger on how, I eventually realised that playing Espalion feels less like flying a fighter ship in a future war and more like taking part in some kind of choreographed performance. The enemies are all arranged into exact positions, and have exact lines of fire to create intricate grids and weaving patterns, in contrast to the chaotic spirals and shapes of typical shooters.
The way it plays is fairly unique, too.Your main (and only) weapon is a pair of two shields that shoot streams of bullets, either in front of and behind your ship, or to either side of your ship. You switch between the two positions at the touch of a button. The shields also absorb bullets, which is also the game's main scoring gimmick. As I said earlier, the game feels like a choreographed performance, in which you're expected to find the right place to be to survive, as well as the right alignment for your shields to both absorb enemy shots and kill those enemies.
The choreographed feeling doesn't hurt the game like you mgiht be thinking, though. It is still a shooting game and quick enough reflexes will get you through, so it's not like a shooting version of Rick Dangerous, with unfair deathtraps that are impossible to avoid on a first attempt.