Sounds: These are obvious programmer sounds, and thats fine for placeholders.
The player based sounds makes me want to mute the sound outright, the 'pew pew' if thats going to be playing whilest i'm shooting all the time will get old very very quickly - it needs to be toned down a little or made into a rolling sound with a bit of a lower pitch, and the hit sound could be muted down a fair amount - at the moment it sounds like two metal poles hitting each other which feels out of place. The same sound coming out of the 'capital ship turret' compared to the 'enemy fighter' would also benefit from being mixed up a little, with the turret being more 'deep' to represent a heavier weapon might help mix up your soundscape.
Movement: I think the movement works well for the retro feel, however i do think your angular momentum cancels out a little too much/too quickly. You have the camera hard locked on your player ship, perhaps give a little 'sway' as you change direction allowing the camera to be off centered to the ship to give the impression that your view is 'catching up' to the change in momentum?
Weapon effectiveness and feedback: I'd like to see some feedback to see how damaged something was, for example, in your video you see the player hit a turret about 8-10 times before it simply explodes. You could take the approach to show the player the damage that they're causing by texturing a 'healthy' enemy differently to a 'slightly damaged' or 'critically damaged' one. Likewise you could do this to the player ship as you have your 'health bar' at the bottom of the screen, but all your action in the middle... you force the player to look to the bottom of the screen to understand how much health they have left, where you could update the texture on your player ship to show holes, or other 'battle damage'.
I'd expect the battlecruiser's weapons to be either more damaging, or more plentiful, than the fighter ships. Variance in the weapons by varying the rate of fire, spread, shot damage, etc, will create a more diverse game for you.