Games like Dog
Games like Dog include Stardew Valley, Maltese's Fluffy Onsen, The Sims™ 4, Unpacking, and Wobbledogs. We matched them by the tags players give Dog on Steam (Casual, Simulation, Dogs, Idler, and Pixel Graphics): closest matches first, and among equally close ones the better-known games.

Stardew Valley
Shared: Pixel Graphics · Simulation · Life Sim

Maltese's Fluffy Onsen
Shared: Simulation · Pixel Graphics · Casual

The Sims™ 4
Shared: Simulation · Life Sim · Casual

Unpacking
Shared: Casual · Pixel Graphics · Simulation

Wobbledogs
Shared: Dogs · Simulation · Sandbox

Cookie Clicker
Shared: Casual · Idler · Pixel Graphics

Sticky Business
Shared: Casual · Simulation · Cute

MyVoiceZoo
Shared: Casual · Simulation · Sandbox

People Playground
Shared: Sandbox · Simulation · 2D

Tiny Pasture
Shared: Idler · Casual · Pixel Graphics

Screen Cat
Shared: Casual · Idler · Simulation

Little Witch in the Woods
Shared: Casual · Pixel Graphics · Simulation

DAVE THE DIVER
Shared: Casual · Pixel Graphics · Simulation

The Sims™ 3
Shared: Simulation · Casual · Life Sim

Paralives
Shared: Simulation · Life Sim · Casual

Potion Craft: Alchemist Simulator
Shared: Simulation · Casual · 2D

Chill Pulse
Shared: Casual · Simulation · Idler

Shelldiver
Shared: Casual · Idler · Simulation

WorldBox - God Simulator
Shared: Simulation · Sandbox · Pixel Graphics

Garry's Mod
Shared: Sandbox · Casual · Simulation

Montaro
Shared: Casual · Dogs · Pixel Graphics

Game Dev Tycoon
Shared: Simulation · Casual · 2D

PowerWash Simulator
Shared: Casual · Simulation · Sandbox

Fields of Mistria
Shared: Pixel Graphics · Simulation · Life Sim