So within "playing now" you dont have "player" and "there"?
In this context, "player" = the client PC, and "there" = server PC.
Yes, I can now confirm that this was the issue. There was no "Player" and "There" options. I now realize you need those options to send playback to another pc (in my case, use the client to send playback to the server pc), but there was no way for me to know that such an option existed, since it wasn't there. You can't know what you don't know, I guess.
What I ended up doing is reinstall jriver on both computers. I noticed that, by default, "Player" is available under Playing Now on both pc's. I added an album on the server pc to create a library, then set up the Media Network. On the client pc, I connected to the server library and eureka, "There" suddenly appeared right below "Player" under Playing Now! I can now control the playback on the server pc using the client pc!
I then tried restoring my full library + settings on the server pc, setup a new Media network. This time, when I connected to the server library from the client pc, "There" did not appear...
Then, I reinstalled jriver on the server pc and restored the full library, but this time, I chose the library only, not the settings. I set up the media server on the server pc once more, connected to the server library from the client pc, and everything works fine, "There" shows up on the client pc. This basically tells me that the issue is related to a setting of some kind in jriver, not the library itself. Perhaps someone with a better understanding can confirm if this is the case?
Anyhow, even though it would've been simpler to figure out how that add "Player" and "There" using my initial library setup, the issue is now resolved. I'm quite happy to now be able to control playback remotely, it is so convenient.
Thanks to everyone for your input, it is greatly appreciated!