Games like Moon and Away
Games like Moon and Away include Firewatch, What Remains of Edith Finch, The Beginner's Guide, Before Your Eyes, and Gone Home. We matched them by the tags players give Moon and Away on Steam (Story Rich, Exploration, Walking Simulator, Philosophical, and Romance): closest matches first, and among equally close ones the better-known games.

Firewatch
Shared: Story Rich · Walking Simulator · Adventure

What Remains of Edith Finch
Shared: Story Rich · Walking Simulator · Exploration

The Beginner's Guide
Shared: Story Rich · Walking Simulator · First-Person

Before Your Eyes
Shared: Story Rich · Walking Simulator · Interactive Fiction

Gone Home
Shared: Walking Simulator · Exploration · Story Rich

Journey
Shared: Exploration · Adventure · Walking Simulator

Amnesia: A Machine For Pigs
Shared: Story Rich · Walking Simulator · Exploration

Outer Wilds
Shared: Exploration · Story Rich · Adventure

The Witness
Shared: Exploration · First-Person · Walking Simulator

The Talos Principle
Shared: Philosophical · Story Rich · First-Person

DEATH STRANDING DIRECTOR'S CUT
Shared: Story Rich · Walking Simulator · Exploration

To the Moon
Shared: Story Rich · Adventure · Romance

The Forgotten City
Shared: Exploration · Story Rich · Adventure

Road 96
Shared: Story Rich · First-Person · Adventure

The First Tree
Shared: Walking Simulator · Exploration · Adventure

Riven
Shared: Exploration · Story Rich · Adventure

CARIMARA: Beneath the forlorn limbs
Shared: Story Rich · Exploration · Adventure

INFRA
Shared: Exploration · Walking Simulator · Story Rich

The Talos Principle 2
Shared: Story Rich · Philosophical · Exploration

Quern - Undying Thoughts
Shared: Exploration · Adventure · Walking Simulator

Fallout 4
Shared: Exploration · Story Rich · Adventure

ABZU
Shared: Exploration · Relaxing · Adventure

Layers of Fear (2016)
Shared: Walking Simulator · Story Rich · First-Person

The Vanishing of Ethan Carter
Shared: Walking Simulator · Exploration · Story Rich