The .bin and .cue file are the parts of the actual game disc that you want. The .bin file contains almost all of the data and the .cue file contains some extra information about the structure of the CD. All the rest is Internet Archive stuff (and an image of the game cover of course).
To open it, you can convert it to a .iso disk image instead, which any Linux distribution can open as if it were a real CD. This blog post talks about how to do that. The last paragraph about mount
you can probably replace with double-clicking the .iso file in the GUI I would guess.
Archive Team often uses the Internet Archive to share the things they save and obviously they have a shared goal of saving a copy of everything ever made, but they aren’t the same people. The Archive Team is a vigilante white hat hacker group (well, maybe a little bit grey), and running a Warrior basically means you’re volunteering to be part of their botnet. When a website is going to be shut down, they’ll whip together a script and push it out to the botnet to try to grab as much of the dying site as they can, and when there’s more downtime they have some other projects, like trying to brute force all those awful link shorteners so that when they inevitably die, people can still figure out where it should’ve pointed to.