Games like Sleeping with the Phish
Games like Sleeping with the Phish include Papers, Please, There Is No Game: Wrong Dimension, That's not my Neighbor, Unpacking, and Gorogoa. We matched them by the tags players give Sleeping with the Phish on Steam (Casual, Simulation, Puzzle, Point & Click, and Singleplayer): closest matches first, and among equally close ones the better-known games.

Papers, Please
Shared: Simulation · Point & Click · Indie

There Is No Game: Wrong Dimension
Shared: Puzzle · Point & Click · Indie

That's not my Neighbor
Shared: Casual · Point & Click · Simulation

Unpacking
Shared: Casual · Puzzle · Simulation

Gorogoa
Shared: Puzzle · Casual · Singleplayer

Game Dev Tycoon
Shared: Simulation · Casual · Indie

The Room
Shared: Puzzle · Point & Click · Singleplayer

Emily is Away Too
Shared: Simulation · Casual · Indie

Youtubers Life
Shared: Casual · Singleplayer · Simulation

Emily is Away <3
Shared: Simulation · Casual · Choices Matter

Deponia
Shared: Point & Click · Puzzle · Singleplayer

Volcano Princess
Shared: Simulation · Life Sim · Choices Matter

Little Inferno
Shared: Casual · Puzzle · Singleplayer

Broken Age
Shared: Point & Click · Singleplayer · Indie

Storyteller
Shared: Puzzle · Point & Click · Singleplayer

Mini Motorways
Shared: Simulation · Casual · Puzzle

Death and Taxes
Shared: Simulation · Choices Matter · Point & Click

Streamer Life Simulator
Shared: Simulation · Casual · Singleplayer

Chinese Parents
Shared: Simulation · Casual · Life Sim

Potion Craft: Alchemist Simulator
Shared: Simulation · Singleplayer · Casual

Malware
Shared: Simulation · Puzzle · Singleplayer

Please, Don’t Touch Anything
Shared: Puzzle · Point & Click · Indie

Mini Metro
Shared: Puzzle · Simulation · Casual

Zup! S
Shared: Casual · Puzzle · Indie