Games like On the Run: Rogue Heroes
Games like On the Run: Rogue Heroes include Roadwarden, The Life and Suffering of Sir Brante, Suzerain, Baldur's Gate 3, and Late Shift. We matched them by the tags players give On the Run: Rogue Heroes on Steam (RPG, Interactive Fiction, Choose Your Own Adventure, Text-Based, and Superhero): closest matches first, and among equally close ones the better-known games.

Roadwarden
Shared: RPG · Text-Based · Interactive Fiction

The Life and Suffering of Sir Brante
Shared: RPG · Interactive Fiction · Choose Your Own Adventure

Suzerain
Shared: Choose Your Own Adventure · Interactive Fiction · RPG

Baldur's Gate 3
Shared: RPG · Character Customization · Choices Matter

Late Shift
Shared: Choose Your Own Adventure · Interactive Fiction · Choices Matter

Choice of Robots
Shared: Choose Your Own Adventure · Interactive Fiction · Text-Based

Vampire: The Masquerade — Night Road
Shared: Choose Your Own Adventure · Interactive Fiction · Text-Based

Tainted Grail: The Fall of Avalon
Shared: RPG · Character Customization · Adventure

Undertale
Shared: RPG · Choices Matter · Multiple Endings

Fallen Hero: Rebirth
Shared: RPG · Text-Based · Choose Your Own Adventure

Dragon Age: Origins - Ultimate Edition
Shared: RPG · Choices Matter · Character Customization

The Witcher 3: Wild Hunt — Remastered
Shared: RPG · Choices Matter · Adventure

The Henry Stickmin Collection
Shared: Choose Your Own Adventure · Multiple Endings · Choices Matter

Aliya: Timelink
Shared: RPG · Interactive Fiction · Text-Based

Breakout 13
Shared: Interactive Fiction · Choose Your Own Adventure · Choices Matter

The Life and Suffering of Sir Brante — Chapter 1&2
Shared: Interactive Fiction · Choose Your Own Adventure · RPG

Legend of Mortal
Shared: RPG · Choices Matter · Multiple Endings

Love Is All Around
Shared: Interactive Fiction · Singleplayer · Multiple Endings

Sorcery! Parts 1 and 2
Shared: RPG · Choose Your Own Adventure · Interactive Fiction

STAR WARS™ Knights of the Old Republic™ II - The Sith Lords™
Shared: RPG · Choices Matter · Singleplayer

Far Away
Shared: Choose Your Own Adventure · Choices Matter · Singleplayer

The Test
Shared: Choose Your Own Adventure · Multiple Endings · Choices Matter

Dragon Age™ Inquisition
Shared: RPG · Character Customization · Choices Matter

Road to Empress I
Shared: RPG · Choices Matter · Interactive Fiction