It is a Linux operating system, either Ubuntu or Arch Linux. With a window manager, most likely AwesomeWM
Window managers are targeted at power users who basically do not want to use a mouse, and optimize workflow with hot keys.
In the scenario you are refering to, all those programs would be seperate processes/applications, tiled and re sized to all fit on the screen. Awesome also disables the ability to resize, instead using hot keys to tile the windows to your liking (half screen, quarter screen, whole screen, etc).
In order to shuffle through the programs, you'd use either alt+tab, like on windows to shuffle through apps, or another hot key that you designate.
You could be working on your code in your text editor... notice you got a chat message and simply press MOD (windows key) + TAB to cycle through your apps. You could also number them, and get to them that way.
This is geared toward 'power' users and people who can really make the most of their systems.
I personally use something similar, although not nearly as crazy. I keep three-five different 'spaces' (each one starts as a seperate, clean desktop) depending on what I'm working on.
My first houses a browser, full screen. The next is a text editor, Atom, at the moment. The editor itself takes up the left half while the menus, orginization, and plug ins and take up a HALF of the other half...
The bottom half of that monitors my Google Drive/Drop Box, because I'm often awaiting files from people I work with.
The next is my email, IRC (from time to time) and system monitors... yknow. To be cool.
There is a strong learning curve, especially since AwesomeWM has to be coded/designed to YOUR liking. Thankfully there is a pretty extensive database/wiki on the subject- so anyone with a weekend to kill could be alt tabbing in no time.
At first it was very frustrating, and I felt so stupid. I ended up completely reinstalling Windows 7 because my *NIX OS felt so silly.
Eventually my curiousity got the best of me and I wanted to try again. So I grabbed an old laptop and went to work.
When I began around noon on a Friday, I knew absolutely nothing about Linux, Awesome, or the LUA programming language. I spent quite a bit of time looking at other peoples desktops, and hoping they left a description of how they did it. Often times, people in the *nix community are very helpful. Once I got an idea of the things I wanted and didn't... I went to work on how exactly I was going to pull it off.
My AWM is heavily modified from the source you download. As time goes on, I modify one thing, change another... before I knew it- it was completely my own. Someone familiar with AWM would still probably have a hard time operating my workstation.
..also, for the record, Tor is short for 'the onion router' which describes the unindexed world wide web...several times the size of the 'indexed' web, or what you can google, basically.
People often call it 'the dark web' because many people use it to buy dirty things, but it was originally developed by the NAVY, soooo...
Tor would help them stay anonymous, putting up proxies between them selves and the outside world. And to dig a little deeper...
In Daniel Berg's book (the one this movie is based on) he explained that their systems were so slow because they used completely virutalized systems. Meaning the actual computer was somewhere far, far away. Probably another country. Then they remoted in and operated it that way. He said often times it would take over an hour to compose a simple email. He also talks about how Julian barely every looked at his screen, but because of the lag, this would cause problems...
He'd be there, typing away furiously, when all of a sudden he'd yell DAMN IT... a mistake from two pages up. They often told him to slow down, but a lot of people felt like he literally couldn't slow down.
They used quite a few different ways to keep themselves hidden, and I thought the movie did an OK job... although 'adding another tor circuit' doesn't mean anything.
hope this... uhhh...answered your question. lol