My take on it, from the viewpoint a non-professional dude who knows nothing about coding and is just assuming...
Firstly, if I understand what you say correctly, you're assuming that the player repeatedly extracts files from an archive. That is half correct and half not. You do indeed create an offline archive in your own computer, that lies within the "assets" folder, where you have your jpg (image) files and mp3 (audio) files.
What actually happens with the player is:
1. Remember the json files you stuck into the "nutaku" folder? Those are like instructions for the "download_assets" program, which will proceed to access the Nutaku server to download said assets into the "assets" folder. Note that it is a download, and therefore you require Internet access at this step.
2. The following 2 programs I assume are to write up the configs such that the assets are actually integrated into the player UI, if you don't run these, nothing shows up (but errors I guess).
3. Accessing the player after you run the programs afterwards is simply like opening a chain of jpg and mp3 files that are already stored in your computer, and therefore is offline access. Think opening a simple word document in your computer. It never spends itself, unless the data has been corrupted.
So to answer your question, do you need to update? Likely no, unless data corruption, which you will know if you see any exceptions happen in the player when normally it runs fine.
But there is a case where the program might not work, and that's if nutaku changes their network request system (or some other bs in their server) that completely invalidates the current method the program requests and downloads assets. If such a doomsday does happen, you would have to rewrite the program to fit into their new system. Or wait for Eliont to make a new player and download it.
Tl;dr... Nope.
Now I shall await crucification from people who actually know programming