The underlying data source is just a YouTube video, so to remove head bobbing, you'd have to apply visual processing algorithms for that (that boil down to computing the most likely global pixel shift frame-by-frame, and shifting the whole video horizontally&vertically to compensate).
They're just Youtube videos so it's going to depend on how it was recorded. There's video reprocessing that could fix that but it's a lot to ask for a little game site to reprocess all the videos.