In contrast to conventional "cloud gaming" solutions, GMT is an engine-specific implementation of P2P lockstep networking - the kind of thing you see in higher-end emulators, fighting games, and some of the online multiplayer mods for games (including mine).
This offers a fairer split of lag between players, lower system/network requirements, and fairer handling of internet connection hickups.
For a slightly more in-depth comparison of netcode options, see this sheet.
As for the technical side, Microsoft Detours is used - if you've ever used software that augments Windows UI elements, this is pretty much the same, except for GameMaker runtime - so, for example, the game might poll Windows API functions for input as usual, but, instead of calling the system function directly, it would instead call GMT's function, which would return synchronized inputs that account for other player.