If you're only interested in games that have an official from-VKB binding or mapping file provided: then it supports none, I guess.
It should work on any game that supports the Windows joystick HID functionality, "out of the box" in the sense of no playing around in the VKB software "required" (aside from calibration!) for any game that supports up to 32 buttons on a joystick.
There might be other users that have bindings files they would share. I personally don't use the Gladiator base, but my Kosmosima Premium grip on my left is I think effectively the same as yours, just reversed perhaps? So page 2 of this might be useful to you as an aid to assigning your bindings in game (don't sweat it if the tiny numbers up in the corner of each block don't match what you see in your in-game binding when you assign it, what matters to you is more associating the physical button to the game action not what the "logical" value was, and I can't know for sure if the firmware for the Gladiator assigns the logical numbers the same as the firmware I was on when I made that for my Kosmosima LH on Gunfighter). If you have powerpoint it's easy enough to mirror the pictures I used, or swap out your own.
https://1drv.ms/p/s!AuHD2NL7qn3w-1iqeIu ... t?e=6XfP5AI currently use it to play Elite Dangerous. Certainly many people also play Star Citizen, DCS, etc. What are your interests? Assigning in-game bindings is generally easy enough, if that's all you want to do. Only need to get into the actual vendor software if you want to play with response curves, program additional options (like a shift button to make all the others have 2 different functions, or a short vs. long press being a different signal on a given button, things like that.
(PS I'm not official VKB at all, just a player myself. I like your idea of them hosting bindings files somewhere but not sure how they can do that since even the 'logical' buttons from the stick can be altered by the user, as I've done for example (one button has a 'tempo' function so I have a short press that's (to Windows) Joy-3, but then a long press of the same button is Joy-33. So anyone without my edits to the stick's config would not be able to trigger the action Joy-33 is tied to in-game. I guess they could restrict hosted bindings files to those that use only the Default stick config...but really the non-defaults are where the fun is all at. ;-D )