Is there a term for controllers with the game built in?

controllers hardware terminology

These are most commonly known as "Plug & Play games", but can also be called "TV games" or "handheld TV games" by some retailers. They are a type of dedicated console.

[Wikipedia]

Related

Is it possible to make armour that can survive /kill?
Name for games that have abusive in app purchases
Name of the mix of PvP and PvE
When are Dive Balls extra effective?
When is the "Exploration Bonus" awarded in Escape from Tarkov?
Scorpion in Injustice : Gods amongs us
How to make a mob spawner that spawns mobs at a specific coordinate?
Polyculture achievement: Is there any way to know which ones I shipped 15 of?
Diablo II Resurrected - Battle.net connection problem
Requirements for completing Star Trek Armada Dark Omens mission?
What do the titles on the team confirmation screen mean?
Name of the song in Amiga game Circus Games?