What's the difference between a labyrinth and a maze? The original, primal Labyrinth - the first in human history - the one from which all others derive - is of course Jim Henson's 1986 David Bowie vehicle. That labyrinth had a thousand paths - that labyrinth was all about choices. But, confusingly, most reference works will tell you that that this is the difference between the two: a maze has choices and many paths, while a labyrinth is unicursal, with a single choiceless path to the centre.
You'll have seen the design of the classical and mediaeval labyrinths - the symmetrical single-path concentric-rings that look like a piece of jewellery or a ball of unusually elegant string. Henson's Labyrinth wasn't like that, and neither was the Cretan one. But they were both designed experiences.
One was intended to bring the protagonist to David Bowie, and the other was intended to feed the protagonist to the Minotaur. Unicursal knot-labyrinths were experiences too - in prayer, in ritual, for luck. Pilgrims shuffled round cathedral labyrinths on their knees; fishermen used them to ensure favourable winds and good catches; Lapp herdsmen walked labyrinths, and I love that I'm writing this sentence, 'to protect their reindeer from the ravages of wolverines'.
Okay, we're drifting off into history here, and away from the main point that you've probably already guessed. The main point is this: games are also designed experiences. And, just like labyrinths, they're spatial experiences.
"Ts'ui Pe must have said once: I am withdrawing to write a book. And another time: I am withdrawing to construct a labyrinth. Every one imagined two works; to no one did it occur that the book and the maze were one and the same thing." - Jorge Luis Borges, The Garden of Forking Paths
All - all - games involve spatial relationships. Often it's tourism, exploring a virtual world. Often it's pacing. Often it's strategic placement. Even in card games, space and positioning are fundamental. Even in choice-based interactive fiction, the placement of links and choices in text is important. Not all decisions in games - probably not even most decisions in games - are spatial ones, but you will be making spatial decisions, constantly, from second to second. What to explore, where to move next, how to reconfigure the relationship of your avatars and tokens.
One of the many brilliant, subtle tweaks from the original X-COM to Firaxis' rebooted XCOM is that the maps are long, not wide. There is a spatial choice to be made from the beginning, but that choice isn't a dozen different directions. It is, more or less, left or right or straight on. XCOM is less of a maze, and more of a labyrinth. Firaxis thought carefully about the choices you'd have from moment to moment, and tuned them carefully to make an intended experience. XCOM doesn't bombard you with demands. It asks you a series of curated questions, many of them encoded in the space around you.
So I'm going to go a bit further than 'labyrinths are designed experiences': I'm going to say that 'a labyrinth is architecture that asks a question.'
Every choice you make in a labyrinth - or a game - is an answer to a question. Every question you answer builds up an experience. The most fundamental and intimate question in a game is: where do you want to go next? We navigate space instinctively - WSAD, left stick / right stick, mouse-click. We answer a series of questions without consciously realising it, and our answers are drawn behind us like a line on a map.
"Everything that you wanted, I have done. You asked that the child be taken, I took him. You cowered before me, and I was frightening. I have reordered time, I have turned the world upside down, and I have done it all for you! I am exhausted from living up to your expectations of me. Isn't that generous?" - Jareth the Goblin King, Labyrinth
A decision is an answered question. Sid Meier (probably the most famous living game designer - and one of the Firaxis founders) issued the dictum (probably the most famous living game design dictum) that 'a game is a series of interesting decisions'. What does this mean here?
A decision does not become more interesting the more options you have, any more than a game becomes better the more features it has. However, a series of layered decisions, one after another, so that each choice is more interesting than the last... now we're talking. This is how the best games work. One of the reason roguelikes are so popular is that they work this way not only at a game level but at a meta level. We build up a kind of superstructure of understanding, from this run and previous ones. This superstructure is like you seeing the labyrinth from above.
Games exist for you. They might look like opponents, they might be challenges, but they need you to complete them. All the tunnels in a labyrinth and all the questions in a game are created in advance. Even procedurally generated content occurs because someone set the rules, six years ago and half a world away. So a game is a conversation between a player and a designer, but it's a conversation where the designer has had to work out their half ahead of time. This is why game design is hard! But it's also why game design is exciting, because you can see the answers people bring to your questions, especially in the age of instant social media.
Every interesting art form depends on the audience bringing something to the experience, but with a game or a labyrinth, that's much more so. The Minotaur has nothing better to do than sit around waiting for you: he only exists so you can decide how to kill him. Every time a guard in Thief says 'Must have been rats', he's wrong. Definitionally, he's wrong. If you weren't there for him to have been wrong about, he wouldn't have said it.
"A man sets out to draw the world. As the years go by, he peoples a space with images of provinces, kingdoms, mountains, bays, ships, islands, fishes, rooms, instruments, stars, horses, and individuals. A short time before he dies, he discovers that the patient labyrinth of lines traces the lineaments of his own face." - Jorge Luis Borges, Dreamtigers
David Mamet once said that the outcome of a plot should be 'both surprising and inevitable'. The same applies to interesting choice outcomes. But both to be surprised, and to know what's coming, we need to see the shape of the world in advance.
That's what game-labyrinths allow. A game is a designed experience: experiences have a duration. A labyrinth is architecture that asks a question: answering questions allows you to establish a context. In a well-designed game, you see the outcome begin to emerge before the end of the experience. You know you're low on food, you know your alliances are fraying, you know you're a hair away from the end of the level, you know what might come next. It might be success or it might be failure, but it will make sense in terms of what came before. It'll seem inevitable.
But of course it won't be inevitable the same way for different people. Making choices in a game is an expression of your identity. A satisfying array of choices lets you express yourself. It responds to that expression. It lets us determine who we are. There is a mountain of hippy crap talked about labyrinths, but here and now I'm going to stand on top of that mountain and say: it's true, you know. If you walk a labyrinth, it teaches you something about yourself.