Don’t most engines offer this by default?

I know Unreal Tournament 99 and especially 2004 was very extensible because they offered uScript (very C++ like) which made it easy to make all sorts of mutators and mods. They even had a specific feature for making in-game cutscenes (I thought it was named Kino but apparently not).

I don’t have much knowledge of Source but afaik they also offered something similar.