Games like Henchman Story
Games like Henchman Story include Undertale, The Henry Stickmin Collection, South Park™: The Stick of Truth™, I Wani Hug that Gator!, and Monster Prom 3: Monster Roadtrip. We matched them by the tags players give Henchman Story on Steam (Visual Novel, Funny, 2D, Comic Book, and Dark Humor): closest matches first, and among equally close ones the better-known games.

Undertale
Shared: Funny · Story Rich · Choices Matter

The Henry Stickmin Collection
Shared: Funny · Comedy · 2D

South Park™: The Stick of Truth™
Shared: Funny · Comedy · Dark Humor

I Wani Hug that Gator!
Shared: Visual Novel · Story Rich · Interactive Fiction

Monster Prom 3: Monster Roadtrip
Shared: Visual Novel · Comedy · Funny

Endless Monday: Dreams and Deadlines
Shared: Visual Novel · 2D · Interactive Fiction

Monster Prom 4: Monster Con
Shared: Visual Novel · Comedy · Funny

Dispatch
Shared: Story Rich · Choices Matter · Comedy

Far Away
Shared: Visual Novel · Choices Matter · Story Rich

There Is No Game: Wrong Dimension
Shared: Funny · Comedy · 2D

Night in the Woods
Shared: Dark Humor · Story Rich · 2D

Mesmalie
Shared: Visual Novel · 2D · Interactive Fiction

Kindergarten 3
Shared: Dark Humor · Funny · Interactive Fiction

Deponia
Shared: Funny · Comedy · 2D

Refind Self: The Personality Test Game
Shared: Visual Novel · Interactive Fiction · 2D

Until Then
Shared: Visual Novel · 2D · Interactive Fiction

Class of '09: The Re-Up
Shared: Visual Novel · Dark Humor · Comedy

Otaku's Adventure
Shared: Funny · Visual Novel · Story Rich

Tales from the Borderlands
Shared: Comedy · Funny · Story Rich

Slay the Princess — The Pristine Cut
Shared: Visual Novel · Choices Matter · Story Rich

LoveChoice
Shared: Visual Novel · Story Rich · Choices Matter

Marco & The Galaxy Dragon
Shared: Visual Novel · Funny · Story Rich

Suzerain
Shared: Visual Novel · Interactive Fiction · Choices Matter

Coffee Talk
Shared: Visual Novel · Dialogue Heavy · Interactive Fiction