This is where the section of the GPL FAQ I linked in an earlier post was good - it explained this very well. Let me explain it in my own way, though:
Suppose there was a phone app for the weather: the part in the phone is the UI, and the weather forecast is obtained by a web service request to a server. The program on the phone would clearly be a different program to the one on the web server. Me putting the phone software under GPL would not oblige the owner of the program running on the server to put that program under GPL.
Other examples they gave of one program using another program as a service included pipes, command prompt etc.
Now take a look at Stockfish NNUE: it is VERY clear that the NN is part of the program. If you fork the program and amend the NN, the NN will STILL be under GPL. There are cases you could argue about, but in this case, from the section of the GPL that I linked previously, there's no room for discussion: the NN and its weights are part of the forked program, and are covered by the GPL.