@thulsadoom42
Welcome to the site !
Idk how things work specifically all that well, I just bang away until it works. Probably not the best approach 
You can have windows and Linux both installed on. I can't remember. I think I had to do some sort of virtual thing. Anyway, I hate windows so I rarely use it. Probably because I don't know how lol
At any rate, it looks like it's the triplea install giving you trouble. As Panther says, triplea should auto add java for you, so should be good there.
When I DL triplea I don't use the installer command. I just go to permissions and hit execute.
I'll DL a prerelease I've been meaning to do and show you how I do it.
I'm gonna DL 15025 as recommended by The Dog. It's the last one that centers on your Capital. You can force individual maps to do it by tweaking the xml but that's a fair amount of work and frankly shouldn't be necessary.
Anyway, it's a nice feature that you take for granted until it's gone. Then it becomes annoying. It's a simple fix but w/e not my department 
Gonna go here for the prerelease
https://github.com/triplea-game/triplea/releases/tag/2.7.15025
you want the unix one as you already know 
Hmm won't let me post the pic. Try a smaller version.

So I have 2 Triplea/triplea folders. One with a Big T, which is where the releases live and one with a small t where the games/maps and saves live.

Here's the Big T

You can see I have 14962 and then another release in a separate folder 15330
I go to downloads and right click on 15025

Go to properties and hit Permissions and then execute

Then open a terminal and drag 15025 into it

hit enter

and then follow the prompts. I usually put it in a different folder 15025 will call it. Have to be careful or you have to type the whole thing in.

Then just keep hitting next

then Finish and it should fire up
You can see the Java version and the triplea version upper left.

Oh yea, I guess I shoulda said this first. I can't get the 2.5 stable to work on linux anymore. Probably a couple years now. I've mentioned it to dan a few times but nothing ever came of it.
This is what happens when I try it

So you can play local or by Forum/email but can't use the lobby. I haven't checked the 2.7 lobby in a while but I think it's still being worked on.
So you will need to use windows to access the lobby. At least that's what I have to do 
Let me know if you get stuck somewhere. We'll call in reinforcements 