The way our brain works is strange. The reason we think that the words are moving, is because we don't recognise the words. The colour change makes our brain tell our eyes to look at it, as it is a new thing, and prevents us always looking at the words. And, as we don't recognise the words, we look at the first two letters, and the last, and try to guess it. If we can't guess, we carry on, but as we're already further to the right, we see the words as moving to the right.
