Some more PS 2 games :

Chou-jikyuu Yousai Macross-Japan only , but with English menus and completely playable ,

Silpheed : The Lost Planet ,

Shadow Of Ganymede ,

XII Stag (pronounced Twelve Stag)-Jap/Eng , shoot 'em , Playable ,

Assault Suits Valken-Jap-Upgraded remake of the original game  for the Super Famicom, released internationally as Cybernator .

More games I forgot to list yesterday:

Robotech: Battlecry (PS2/GC)

Armada (DC)

Battle Ace (Supergrafx/PC Engine), on-rails shooter

Astro Trooper Vanark (PSX), a rather lame attempt at mixing Starfox and Resident Evil-like adventure complete with tanky character control

Bulk Slash (Saturn), third person shooter with transforming mechs

Cybermorph (Jaguar), Jaguar's entry title which responsible for "Where did you learn to fly?" meme

Mobile Suit Gundam: Gihren no Yabou series (various), an extremely complex grand strategy game based on the Gundam's original Universal Century universe. Totally in moonrunes though so much knowledge about both Japanese and Gundam universe are necessary.

The Seed: Warzone (PS2), highly obscure PS2 space RTS where you can design your own spaceships, too bad you can't even command them in the battle however you can give them orders/tactics before the battle (think Gratuitous Space Battles)

Infinte Space (NDS). Not to be confused with the "other" Infinte Space title, this is a story-heavy SRPG with extensive ship customization. Ships designed by the same guy who did Strike Suit Zero designs.

Added a few more but I think a lot of then are more 3D shmup.

Got a few to add to this, Rebel Galaxy outlaw and Everspace to the PS4 and Everspace to Xbox 1.

A new console in the shape of the Switch which has Everspace and Starlink and the wiiU had Starfox Zero.

Also found another game for the PS1 called "Raven project" never heard of it but looks like a space shooter with comical FMV bits.