Games like Rivals
Games like Rivals include No Case Should Remain Unsolved, Firework, OneShot, Blue Prince, and Phoenix Wright: Ace Attorney Trilogy. We matched them by the tags players give Rivals on Steam (Investigation, Visual Novel, 2D, Story Rich, and Puzzle): closest matches first, and among equally close ones the better-known games.

No Case Should Remain Unsolved
Shared: Investigation · Visual Novel · Puzzle

Firework
Shared: 2D · Puzzle · Indie

OneShot
Shared: Story Rich · Indie · Puzzle

Blue Prince
Shared: Investigation · Puzzle · Story Rich

Phoenix Wright: Ace Attorney Trilogy
Shared: Visual Novel · Story Rich · Singleplayer

Murders on the Yangtze River
Shared: Puzzle · Story Rich · Investigation

Papers, Please
Shared: Indie · Singleplayer · Puzzle

The Case of the Golden Idol
Shared: Investigation · Puzzle · Story Rich

Far Away
Shared: Visual Novel · Singleplayer · Story Rich

Sanfu
Shared: 2D · Puzzle · Visual Novel

Milk outside a bag of milk outside a bag of milk
Shared: Visual Novel · Story Rich · Indie

OPUS: Echo of Starsong - Full Bloom Edition
Shared: Visual Novel · Story Rich · 2D

Sally Face - Episode One
Shared: Story Rich · Indie · Puzzle

Tiny Bunny
Shared: Visual Novel · Story Rich · 2D

There Is No Game: Wrong Dimension
Shared: Puzzle · Indie · Story Rich

Lay a Beauty to Rest: The Darkness Peach Blossom Spring
Shared: Visual Novel · Investigation · Story Rich

Murder by Numbers
Shared: Investigation · Visual Novel · Puzzle

Undertale
Shared: Story Rich · 2D · Singleplayer

Servant of the Lake
Shared: Puzzle · Story Rich · Indie

Tangle Tower
Shared: Visual Novel · Puzzle · Story Rich

OPUS: The Day We Found Earth
Shared: Visual Novel · Story Rich · Puzzle

The Death Game Report
Shared: Puzzle · Investigation · Story Rich

Limbus Company
Shared: Story Rich · Visual Novel · Singleplayer

Helltaker
Shared: Puzzle · Indie · 2D