Is it possible to stream media to PlayStation 4 without a computer being connected to internet?

I have a 2TB hard drive with videos in it and it is connected to an AirPort Extreme router via USB. I can watch videos on the PS4 perfectly through the router as long as the computer is on. Is there a way to remove the “middle man” (computer) so I could stream:

PS4 <-> Router <-> HDD

Everything works fine. I just don’t want to waste electricity with the computer having to be on. Also the PS4 is connected to the router via ethernet cable.

I highly recommend you review the documents that explain how Plex works.

https://support.plex.tv/hc/en-us/articles/200288286-What-is-Plex-
https://support.plex.tv/hc/en-us/articles/200375666-Plex-Media-Server-Requirements