Unfortunately those aren't just files that you can easily access. If you do have access to the phone that way, you might be able to back up the contacts using Samsung Kies (Smart Switch is the current version, but not sure if it'll work with older models).
Also, if the screen is dead but the touchscreen isn't, you can connect the phone to a TV using an MHL Cable that's compatible with the S4. That way you can see the screen on the TV and use the touch input to back up the contacts to a cloud service (like Google) or to export them to a VC File.