Within a View, How do i paginate the content found inside a single Multiple file field, i.e. inside one node
There are two obvious ways to solve this, the easier one is through your existing Content views, and the other is through creating a new File type view. 

Content type Views

It is true that the Views type determines what will go into each new row in views results, and Pager is acting on views rows. 

But if you have a multi-value field it is possible to make it display each value in a separate views row, making the same node appear many times in the views results, as many times as there are field values. 

Here's how you do it: 


Edit your "Videos" field and under Multiple field settings make sure you don't have the Display all values in the same row option enabled. 


This will make the same node repeat as many times as you have videos, and although the Pager will still work on node rows, it will look like it's working on field values (if you're only showing that one field and not revealing the node Title, for example). 

File type Views

To get the Pager to actually page through individual files you have to create File views. There are some steps how you can make that views pull data from one content type and field: 


The File views starts by displaying file names of all the files on the system. To make it aware of where the file is being used (you want only the Videos) add a Relationship File: Content using Videos and make it required. This will filter out only the files that are in the "Videos field", and it will make available various Content related Fields and Filters. 
Add the "Content: Videos" Field and set it so it doesn't display all values in the same row. You will still see the files repeated in the results.
Don't add any File Fields 
Under Query settings enable Distinct and Pure distinct. This will make each file display only once.
Add the Contectual filter for NID, it will be available because of the Relationship you added and it will use it by default.