Minecraft has a very basic "electronics" system called redstone that allows you to create basic structures like AND/OR/XOR gates with various wire, torches (devices that power other things), switches and buttons. What they did is take this basic system and make a game that runs within the game using them.

There are some mods for the game that give easier access to higher level structures (single block gates, for example), so it may have used those but I can't tell from this page.