Well, after about 15 minutes of playing my high score was 6... The controls do feel much tighter on the executable version over the web version though.
This is an amazing game! The visuals, while simple, show almost everything I want to see. And the music is perfect.
A few comments small adjustments that I think would make the game even better (albeit easier, so this might have been a purposeful design choice on your part).
1) Enlarge the field of view slightly. At least to me, the game feels somewhat cramped (particularly the web version) A few times my bullet went off screen and I would teleport to it, only to be hit immediately by an enemy I could not see.
2) Add a visual cue showing whether the bullet has been fired or not. A few times I thought I had recalled my bullet but it was still fired, but off-screen. A small empty hole in the player would serve this purpose well I think.
Great job!