Games like The Woods
Games like The Woods include Firewatch, The Beginner's Guide, Layers of Fear (2016), What Remains of Edith Finch, and Outlast. We matched them by the tags players give The Woods on Steam (Indie, First-Person, Horror, Walking Simulator, and Short): closest matches first, and among equally close ones the better-known games.

Firewatch
Shared: Walking Simulator · First-Person · Atmospheric

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

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

What Remains of Edith Finch
Shared: Walking Simulator · First-Person · Atmospheric

Outlast
Shared: First-Person · Horror · Atmospheric

Poppy Playtime
Shared: Horror · First-Person · Indie

The Room
Shared: Indie · Atmospheric · Horror

Mouthwashing
Shared: Horror · Indie · Atmospheric

Among the Sleep - Enhanced Edition
Shared: Indie · Horror · First-Person

Iron Lung
Shared: Horror · Indie · Atmospheric

No, I'm not a Human
Shared: Horror · Indie · First-Person

Five Nights at Freddy's
Shared: Horror · Indie · First-Person

Slender: The Arrival
Shared: Horror · First-Person · Indie

Gone Home
Shared: Indie · Walking Simulator · Short

Phasmophobia
Shared: Horror · First-Person · Supernatural

Amnesia: A Machine For Pigs
Shared: Horror · Walking Simulator · First-Person

The Room Two
Shared: Horror · Indie · Atmospheric

Garten of Banban
Shared: Horror · First-Person · Indie

Buckshot Roulette
Shared: Horror · First-Person · Indie

From The Darkness
Shared: Horror · Indie · First-Person

MiSide
Shared: Horror · First-Person · Atmospheric

Still Wakes the Deep
Shared: Horror · First-Person · Walking Simulator

The Hat Man: Shadow Ward
Shared: Indie · Horror · First-Person

The Park®
Shared: Horror · First-Person · Walking Simulator