Testing conditions (Updated 07/31/2016):

1. I used a desktop PC with no internet access.
2. I installed Linux Mint 17.3 on it.
3. I hooked up an external hard drive with DRM-free copies of Linux games I bought from
GOG.com, Humble Store, IndieGameStand, and Desura.
4. I installed the DRM-free copies of the Linux games to the desktop PC with Linux Mint 17.3 as
the operating system.
5. I launched the games to test which games would work without needing anything extra.

Verdict:
Some games worked without needing anything more than the game itself. Others needed additional
packages, via “Software Manager” (internet connection), for launching or installing them.

Games that worked needing no additional packages or applications:

Armed Seven* (Humble Store)
Art of Fighting* (Humble Store)
Blazing Star* + (Humble Store)
Cave Story Plus* (Humble Store/freeware version)
Doom/Doom II/TNT/Plutonia (GOG, via ZDoom for Linux)
Duke Nukem 3D Atomic Edition (GOG, via the included DOS Box)
Garou: Mark of the Wolves* + (Humble Store)
Gigantic Army* (Humble Store)
King of Fighters 2000* (Humble Store)
King of Fighters 2002* (Humble Store) -best KOF since KOF98!
La Mulana* (Humble Store)
Megabyte Punch* (GOG/Humble Store/IndieGameStand/Desura)
Metal Slug 3* + (Humble Store)
Monaco (Humble Store)
Nuclear Throne* (Humble Store)
Pulstar* (Humble Store)
Quake (GOG, via QuakeSpasm for Linux)
Quake III (GOG, via ioQuake3 for Linux)
Race The Sun* (GOG/Humble Store/IndieGameStand)
Real Bout Fatal Fury 2* (Humble Store)
Retro City Rampage* (GOG/Humble Store)
Rise of the Triad: Dark War (GOG, via the included DOS Box)
Samurai Showdown V* (Humble Store)
Shadow Warrior Classic (GOG, via the included DOS Box)
Shock Troopers* (Humble Store)
Shock Troopers II* (Humble Store)
Strife (GOG, .wad file via Zdoom)
Strife Original (GOG, via ZDoom for Linux)
Symphony (Humble Store)
Torchlight 2 (GOG/Humble Store)

*Works with Logitech F310 set to XInput.
+Includes DRM-free Android APK file.

FYI, the game pages list the required dependencies needed in the Linux system requirements.

It goes like this:

kernel abi - glibc - subsystem libraries - regular libaries - application.

Fortunately, Linux kernel ABI hardly changes, otherwise the game would absolutely not run.
The glibc system c library does change. That causes the game to not run at all, unless older ld.so are shipped statically with the package.
Subsystem libraries rarely change, but when they change, there are also major issues. For example, the migration from OSS to Alsa and then basically to PulseAudio. Very old games still rely on OSS for the sound and Alsa (and Pulse) OSS emulation is quite limited, for example the corresponding wrapper libraries may not exist in 32bit and 64 bit favor at same time, which makes a 32bit game impossible to get sound on 64bit system. However, with something like osspd (oss proxy daemon) its becomes possible.
The very same is applicable for graphical server changes. Current Xorg ABI is not compatible with older ABI, so games are often shipped with older libraries. Soon, Xorg will be replaced with Wayland and there will be some kind of emulation required.

Thats the disadvantage of proprietary code. Only authorized can modify and adapt code for changes in architecture, and even then they often have a limited time window.

Thats why actually running a game inside re-mapper like Wine/PlayonLinux/CrossoverGames or emulator like Dosbox is more preferrable than natively - if its proprietary application, that is.

Fortunately, there is a solution to everything except the Linux kernel ABI issue; run the game inside a chroot. If you need to, just make a chroot (use a distro/architecture combination that is known to be able to run the game), and install the game inside a chroot. With the proper bind mounts and permissions, you can get a game from inside the chroot to run.

If the Linux kernel ABI is an issue, which is extremely unlikely (Linus Torvalds has a strict policy of not breaking userspace), you will need to use a virtual machine, and the problem with doing that is that you lose 3D acceleration unless you are able to do VGA passthrough. VGA passthrough might not be ideal, even if you can do it, because an older kernel will not have any drivers for newer video cards.

Yet consider one thing - Windows games often break ABI on Windows too. For example, when DirectDraw was completely slowly, but then completely removed, and emulation (which is really using same older libraries from backyard) was also removed from Windows.

The Wine magic is also switching different ABI featureset based upon Wine version and what Windows version its set to emulate. Basically, Wine is doing the same thing - replacing the libraries, when you pick different winelib version or change what Windows version you select.

There is really no real way out of it except rewritting the binaries code for more modern ABI/API, but even lack of interest may kill the thing even if its totally open.

PS
UT99/2k4 are awesome, yay!

Thank you for the info, nate1222. Please keep updating this list. Oh, good thinking. And GOG could distribute a tar file with the game.

I prefer the .sh files. Just right click, select Properties, select Permissions, set for "Allow executing files as Program". I also use it for running QuakeSpasm and Nexuiz Classic's .sh launchers.

Both GOG and (to a lesser extent) Humble Store are good on using the .sh files for Linux games.

Will do, and just did. I hammered out a few more games last night.
I work graveyard shift, so I'm usually up during the wee hours.

Quake III Metal Tech v20 mod on Linux!
Metal Tech v20 works with ioQuake3 on Linux Mint!
But, you must have Wine installed.

Metal Tech v20 mod can be found here: http://www.moddb.com/mods/metal-tech-v20-revolutions/downloads/metal-tech-v20-revolutions The installation instructions are en espanol.

After downloading MetalTechv20, do as so:
1. Launch MetalTechv20 via Wine.
2. Set your installation path.
3. Install path should be set to:
/
Home
ioquake3
baseq3

Enjoy!

Native Linux games I tested on Zorin OS 9 Core 64 bit:

[without updates, graphics drivers, nor access to the repositories]

Blazing Star* (Humble Store)
Doom/Doom II/Plutonia/TNT (GOG via ZDoom for Linux)
Garou: Mark of the Wolves* (Humble Store)
Heretic (CD ROM via ZDoom for Linux)
Hexen (CD ROM via ZDoom for Linux)
King Of Fighters 2002* (Humble Store)
Last Blade* (Humble Store)
Metal Slug 3 (Humble Store)
Pulstar* (Humble Store)
Quake III Arena (GOG via ioQuake3 for Linux)
Retro City Rampage DX* (GOG/Humble Store)
Sengoku 3* (Humble Store)
Shock Troopers* (Humble Store)

*Works with the Logitech F310 set to Xinput.

_______________________________________________________________________________________________

Zorin OS 9 Core 64 bit runs Unreal Tournament GOTY (GOG version) right outta the gate!

Testing conditions:
I installed Zorin OS 9 Core 64 bit.
I made certain to not be connected to the internet: no repository access.
I plugged in my external hard drive.
I copied the GOG (DRM-free) version of UTGOTY unto the PC with Zorin OS 9.
I used Wine* (which is included with Zorin OS by default) to install UTGOTY.
I ran UTGOTY.

UTGOTY worked like a charm.
The only drawback was the resolution being capped at 1024x768, due to not having graphics drivers installed.

*Zorin OS comes with Wine by default, without the need to access the repositories.

Zorin OS can be found here: http://zorinos.com/#

You sure like the Humble store. :-)

How do you compare Mint to Zorin?

I take Mint over Zorin. Simply because it's so easy for a former windows user (like myself) to use and is based on Ubuntu 14.04. Though Zorin is pretty good for running older Windows based stuff right outta the gate, as it comes with Wine by default.

And, Hell yeah, I like the Humble Store. I love DRM-free and I've grown to love Linux. GOG is still my go-to site for games. But sometimes Humble Store edges them out in (1) selection and (2) Linux versions of my favs.

(1) The Neo Geo 25th anniversary collection, over 20 friggin' arcade classics, among others.
(2) Nuclear Throne, among others.

And its support for the games? If the game does not run correctly, do they help you or redirect you to the publisher or developers?