Games like Drunk But Not Wasted Knight
Games like Drunk But Not Wasted Knight include Undertale, I Wani Hug that Gator!, The Henry Stickmin Collection, Dispatch, and Suzerain. We matched them by the tags players give Drunk But Not Wasted Knight on Steam (Visual Novel, Choices Matter, Multiple Endings, Dark Humor, and Comedy): closest matches first, and among equally close ones the better-known games.

Undertale
Shared: Choices Matter · Multiple Endings · Story Rich

I Wani Hug that Gator!
Shared: Visual Novel · Choices Matter · Story Rich

The Henry Stickmin Collection
Shared: Multiple Endings · Choices Matter · Comedy

Dispatch
Shared: Choices Matter · Story Rich · Comedy

Suzerain
Shared: Visual Novel · Choices Matter · Multiple Endings

Monster Prom 3: Monster Roadtrip
Shared: Visual Novel · Choices Matter · Comedy

Sovereign Tower
Shared: Choices Matter · Visual Novel · Medieval

Monster Prom 4: Monster Con
Shared: Visual Novel · Comedy · Choices Matter

LoveChoice
Shared: Choices Matter · Visual Novel · Multiple Endings

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

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

Class of '09: The Flip Side
Shared: Visual Novel · Comedy · Multiple Endings

The Life and Suffering of Sir Brante
Shared: Choices Matter · Visual Novel · Story Rich

Coffee Talk
Shared: Visual Novel · Dialogue Heavy · Story Rich

The Wolf Among Us
Shared: Multiple Endings · Choices Matter · Visual Novel

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

Emily is Away <3
Shared: Choices Matter · Multiple Endings · Casual

Scarlet Hollow
Shared: Visual Novel · Choices Matter · Multiple Endings

Volcano Princess
Shared: Choices Matter · Multiple Endings · Visual Novel

The Life and Suffering of Sir Brante — Chapter 1&2
Shared: Visual Novel · Choices Matter · Interactive Fiction

Endless Monday: Dreams and Deadlines
Shared: Visual Novel · Choices Matter · Multiple Endings

Fever Meme
Shared: Comedy · Multiple Endings · Choices Matter

The Test
Shared: Multiple Endings · Choices Matter · Story Rich

The Test: Hypothesis Rising
Shared: Choices Matter · Multiple Endings · Visual Novel