Games like Brinkmanship
Games like Brinkmanship include The Invincible, Firewatch, The Stanley Parable, Before Your Eyes, and Nobody Wants to Die. We matched them by the tags players give Brinkmanship on Steam (Interactive Fiction, Walking Simulator, 3D, First-Person, and Adventure): closest matches first, and among equally close ones the better-known games.

The Invincible
Shared: Walking Simulator · Adventure · Choices Matter

Firewatch
Shared: Walking Simulator · Adventure · First-Person

The Stanley Parable
Shared: Walking Simulator · First-Person · Indie

Before Your Eyes
Shared: Interactive Fiction · First-Person · Walking Simulator

Nobody Wants to Die
Shared: 3D · Detective · Interactive Fiction

CARIMARA: Beneath the forlorn limbs
Shared: Adventure · 3D · Walking Simulator

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

Kona
Shared: First-Person · Adventure · Walking Simulator

Road 96
Shared: First-Person · Adventure · Choices Matter

Return of the Obra Dinn
Shared: Detective · First-Person · Indie

The Forgotten City
Shared: Adventure · First-Person · Choices Matter

Poppy Playtime
Shared: First-Person · Free to Play · Adventure

Mirror 2: Project X
Shared: 3D · Interactive Fiction · Multiple Endings

Road 96: Mile 0
Shared: Interactive Fiction · Walking Simulator · 3D

Gone Home
Shared: Walking Simulator · First-Person · Indie

Killer Frequency
Shared: Interactive Fiction · Adventure · Walking Simulator

Outer Wilds
Shared: Adventure · Space · Mystery

Halo Infinite
Shared: Free to Play · First-Person · Sci-fi

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

Tacoma
Shared: Walking Simulator · Adventure · Indie

Five Nights at Freddy's: Security Breach
Shared: First-Person · 3D · Adventure

The Vanishing of Ethan Carter
Shared: Walking Simulator · Detective · First-Person

Love Is All Around
Shared: First-Person · Interactive Fiction · Choices Matter

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