Like for Wind Waker, the ending credits (while excellent) is 524 MB, and all the videos that play in Mario Kart Wii (some being duplicates at SD [standard definiton?] or say 50 [FPS?]) take up 1.7 GB of storage. I can't imagine how much all the tutorial videos take up on Skyward Sword and language files of Xenoblade Chronicles.
Is there a way to remove these video files from the game and still have them playable?
Removing them isn't too hard. Extract the game by going to Dolphin's game properties, right-clicking on the disc (the topmost item) in the file system tab, and selecting Extract Entire Disc. Then you can play the extracted game by launching its boot.dol file, and deleting files in the extracted structure is easy. But the part of the game that uses the video will likely break. So for instance, for Wind Waker, the game will probably crash when you get to the ending.
The dual audio in Xenoblade Chronicles is what pushed it from a single layer disc to a dual layer disc, by the way. The original Japanese release, which only had Japanese audio, was a single layer disc.