Well, the subtitles aren't part of the video, they are laid over the prerendered movies in the same way they are laid over real time movies. Not to mention that most companies in video games & anime have wordless versions of movies, such as openings and endings, for when something is released in another language.
Its usually simple to tell the pre-rendered scenes from the in-game ones, such as CG graphics or graphics not used in-game, like the PS2 quality graphics used in Days' cutscenes. However, others can be hard to recognize, such as the scene before the 1000 Heartless Battle in Kingdom Hearts II, although it looks like real time, it is actually prerendered so that all the character models could fit in the scene. You can tell its prerendered because of Sora using the Kingdom Key no matter what Keyblade is currently equipped. On the PSP, there are telltale signs of prerendered scenes using real-time models because they will look "JPEGie" for some reason.