In the game there is a resource known as redstone. It can be acquired underground when mining in the game or made available in the game's creative mode. With it you can build various kinds of circuits. The game also includes various input and output blocks, such as buttons, switches, lights, and pistons. Put together, the player can do anything from as simple as a button opening a door to as complex as the article describes.
So... did this kid assemble the whole thing manually brick-by-brick, or did he use some kind of compiler? Does minecraft have macros? Stored procedures? Hard to believe every individual brick was placed by hand.
No macros or compilers per se. There are map editors that allow you to make copies of existing groups of blocks, like replicating seven-segment displays.
There are not really any repositories of existing designs, so the logic was probably all done 'by hand'.
He probably either used Creative Mode (unlimited stuff), peaceful difficulty (no enemies) + a superflat world (don't have to mine things out of your way) or mcedit, which lets you edit map files out-of-game and place whole sections of stuff based on schematics.
Most likely he used an out-of-minecraft editor to put together logic gates that can be copy/pasted, and then larger structures. The map format for minecraft is pretty easy to edit, and there are CAD like programs that'll build out an environment you want.
There is a Lua-based scripting mod but I doubt it is commonly used for things like this. As another commenter mentioned the use of copy-and-paste mods is much more likely.
You can build any logic gate you want, with layout being the hard part (just like IRL...). You can build a computer in Minecraft if you want to. I believe that several people have [1].
To be honest, I think it's a great way to learn about electronics. I know what all the gates do from having taken EE classes, but Minecraft has made some of them a bit more intuitive. Maybe it's just because you can see the things being energized/de-energized, but it does help me think about the different gates/latches/etc. and their interactions.
[1] This is but a small sample of things that might be called computers that have been built in Minecraft:
There’s a redstone resource, which you can lay down as wires. These behave like electronic circuits. There are some special blocks like redstone torches and repeaters.
Some other blocks can be powered or triggered by redstone, for example pistons that push blocks, doors and item dispensers.
There are a variety of switches and buttons, wire, NOR gates, and a small handful of mechanical devices, the most important of which are pistons that allow you to move blocks around.