No i never say that but game dev with long history of using their own in house game engine should continue to use their own develop engine instead of switching
Example if Rockstar game probably the biggest game dev on the planet were to no longer used their in house engine for GTA 6
instead switch to UE5 it would be the end of all in house engine everyone will be using UE5 and paying Epic Games royalties
GTA 6 is another 100 million plus seller so do the math 100 million plus games sales in royalties goes to Epic Games for using their engine Epic would make so much from every dev using their engine that why it can be consider a monopoly
The word is so badly used here that I struggle to comment on the premise of the OP.
It's the most used engine by virtue of being the best, most dev friendly, most capable, most supported engine. There was no market assimilation, no buying other engines, no using an hardware or otherwise market advantage to push for it. Its success happened organically and in no way shape or form should be seen with the word monopoly in mind.
Also, the engine won't make a game look a certain way, devs do that, artists do that.
Having and engine monopoly is almost impossible. To even make the arguement that UE is getting close to a monopoly you'd have to ignore half the industry. Unity is still a big deal and commonly used by indies.
Independent engines are also quite prevalent and produce impressive stuff, RE engine, Slipstream, ID, Northlight etc.
They own the biggest chunk of the market but not even really close to a monopoly.