Games like Chaotic Pursuit
Games like Chaotic Pursuit include Minishoot' Adventures, Chippy, Bit Blaster XL, BALL x PIT, and Nova Drift. We matched them by the tags players give Chaotic Pursuit on Steam (Action, Top-Down Shooter, 2D, Cute, and Cartoony): closest matches first, and among equally close ones the better-known games.

Minishoot' Adventures
Shared: Bullet Hell · Cute · Twin Stick Shooter

Chippy
Shared: Top-Down Shooter · Bullet Hell · Shoot 'Em Up

Bit Blaster XL
Shared: 2D · Shoot 'Em Up · Action

BALL x PIT
Shared: Action · Top-Down Shooter · Bullet Hell

Nova Drift
Shared: Shoot 'Em Up · Bullet Hell · Action

Planes, Bullets and Vodka
Shared: Action · Shoot 'Em Up · 2D

Beat Hazard
Shared: 2D · Shoot 'Em Up · Action

State of Anarchy: Master of Mayhem
Shared: Action · Top-Down Shooter · Shooter

Cyberhunt
Shared: Action · 2D · Shoot 'Em Up

Escape From Duckov
Shared: Action · Top-Down Shooter · Shooter

SNKRX
Shared: Top-Down Shooter · Shoot 'Em Up · Action

Touhou Koumakyou: New Classic - the Embodiment of Scarlet Devil
Shared: Action · Shoot 'Em Up · Bullet Hell

12 is Better Than 6
Shared: Action · Top-Down Shooter · Shooter

Relic Hunters Zero: Remix
Shared: Action · Top-Down Shooter · Twin Stick Shooter

Time Wasters
Shared: 2D · Bullet Hell · Shoot 'Em Up

LUFTRAUSERS
Shared: Action · 2D · Bullet Hell

Vampire Survivors
Shared: 2D · Bullet Hell · Action

DoDonPachi Resurrection
Shared: Top-Down Shooter · Action · 2D

Touhou Kouryudou ~ Unconnected Marketeers.
Shared: Action · Shoot 'Em Up · Bullet Hell

X Invader
Shared: Top-Down Shooter · Shoot 'Em Up · Bullet Hell

Rocket Rats
Shared: 2D · Action · Bullet Hell

Voidigo
Shared: Top-Down Shooter · Shoot 'Em Up · Twin Stick Shooter

Sky Force Reloaded
Shared: Top-Down Shooter · Action · Shoot 'Em Up

ShellShock Live
Shared: Action · 2D · Shooter