There are so many great arcade-style shoot em ups (shmups) on the PlayStation 4. And many got a physical release! 

GAMES SHOWN:

Shikhondo – Soul Eater

Battle Garegga

Raiden V

Pawarumi

Ketsui Deathtiny

R-Type Dimensions EX

Psyvariar Delta

ESP Ra.De. Psi 

Dangun Feveron

Sisters Royale

Sine Mora EX

Dimension Drive

Caladrius Blaze

Jamestown+