Okay, I will attempt to form some kind of answer that makes sense, perhaps it helps :)
So basically to fumble in this specific case could and should mean to stumble over or to trip over something.
Therefore, "Fumbling over the words" could simply imply to not be able to find the right words to say (or write).
It could mean that someone is struggling to pick and choose the correct words to say (or write), or perhaps that there is an abundant amount of words to choose from, but the person is uncertain which ones to choose. Technically, they are fumbling over them.
Here's a random usage of the word fumbling with this same context:
"He was fumbling about in the dark like a headless chicken."