So as my first game purchased on GOG, Star Wars Jedi Knight: Jedi Academy, I wanted to know if there was a way for me to place the game and it's content onto a USB where i'd play it on another computer (without the need for a client). I want to know if it's possible, and if so, how would one go about doing this procedure. Your help would be much appreciated.

Just download the offline installer, then you can put the install files wherever you want. No client or internetconnection needed.

Under big blue download button there is also section called "download offline backup game installers". They are good old regular installers. They install game in its entirety and don't require any internet connection to run and play. You can place the installer on a USB stick and move it to another computer and then install the game.

Edit: You can also use Galaxy do download offline installers.
https://support.gog.com/hc/en-us/articles/212185369-How-can-I-download-standalone-installers-and-bonus-content-with-GOG-Galaxy-

Edit 2: Oh, I may have not understood you correctly. I don't have the game so I can't check if you can run it directly from USB stick...

Why not? Heck, I'm typing this message on a laptop running the entire OS off of USB. And games too. Including Quake 3 engine games (though I haven't run Jedi Academy in particlar).

It's not always just a case of copying install files to a USB though. There are registry entries, required dependancies, save locations etc.
Best way is to download the installers and then install it where you want to play the game. If you want a portable install then there are loops to jump through, and you will want a speedy USB as well.

OpenJK might help with getting things on a stick, but I guess you could just go ahead and use the regular installer and still get away with it - never tried it myself. id Tech 3 based games tend to be rather portable.

Oh, so things like GOG downloader? If so, that shouldn't be a problem.

I don't know gog downloader. Programs have dependancies, c++ extensions, directx, etc. These need to be present on th me host machine to work, or also be portabilised. For instance if I took a java game on USB to a computer without the java virtual machine it wouldn't run. All these things are done by the installer at install time and reg entries are set so programs can find things.
That's not to say things can't be portabilsed, it's not as simply as copy and paste.