Use the 3Cs
In video game design, the 3Cs or "character-camera-controller" is a very important concept to get a hold of. While the terms are specifically thought for video games, they also apply to an extent to any kind of game, computer or not. The general goal is to focus on what the aliens would do to have the best game experience they can.
In short, what information the game gives to you? What do you see, hear, smell, feel or even taste? If your aliens are very different, they will use different canals than humans to receive these feedbacks. The more the canals used will be different from our favored ones, the stranger your game will look. In other words, reduce to the maximum the usage of sight, hearing and touch (in this order of priority) to favor other feedbacks.
Some examples :
- Your alien is a shark capable of electroreception 🦈? It's only normal that they use this as one of the many game feedbacks.
- Use fragrant smells or even let them be tasted to identify the game elements or effects.
- It works even with a softer approach : only using abstract, eerie sounds to play, you're sure to have a chill going up in one's spine.
People interact with games, how do they do it? Do they move a piece on the board, do they change the board itself? Or is it a conversationnal game, where you speak to others to play? You get a lot to play with here : Your aliens will use what is the easiest for them to interact with the game. This goes as broad as the principle itself (moving, touching, speaking...) to as detailed as how a piece can be handled. It also includes how many things you can do at once, so play with this too!
Some examples :
- Multi-brained octopuses with many tentacles will want a specific game space and pieces to play comfortably 🐙, but at the same time they would do multiple things at once to challenge them.
- A trumpet alien will play a melody to interact with the game.
- The electroreceptive sharks will pay attention to their own electric signals when playing shark-poker!
Who you are, in the game? What is representing you in the game and what is it able to interact with, from an inside-the-game perspective? A set of chess pieces with different movements and killable instantly? A number of hitpoints, mana and cards in hands to play? A top hat on the street, with stacks of cash at hand? Piles of seeds and 6 aligned holes? This is where the culture will shine the most : Your avatar, your representation of the game is in abstract what you experience in the world.
In the above examples chess is an abstraction of medieval warfare; Magic: the gathering a battle between two mages with cards giving an emphasis on wild fantasy imagination; Monopoly a capitalist game at core; Oware is a game where there's not a winner in the traditional sense, only players sharing their food stocks.
Some examples (again!) :
- If your sharks are very religious, your game will have their dogmas through their character (priests...) and actions (seek god redemption, ...)
- If your octopuses are peaceful, it will focus on cooperative thinking, sharing resources with each others. Being multi-brained, it wouldn't be surprising such octopuses control multiple characters either, or that characters act on multiple dimensions in order to satiate their superbrains's power.
Alter the verbs
To further extend and alter the viewpoint, use the game's verbs principle. Most human games follow codes, genres, which can be defined by a set of simple verbs. A car race is simply "moving" fast to "reach" the destination 🚗➡️🎯. Chess will be roughly akin to "plan" your "moves" and "attacks" in order to "capture" the king1. Notice that there's always an action and an overarching goal : You do something in order to reach a goal. Be sure to always have this, otherwise your game will lose all its meaning.
Now, take a genre you like, check the verbs used in it and alter some of it. Taking the racing game as example : "Move" to "reach" the destination... What if, to reach the destination, we're not "moving", but "spreading", like some goo expanding over the place? With chess, would it be interesting if your goal was not to "capture" the king, but to help it "copy" itself? And so on. The more imaginative your verbs will be from the original genre's ones, the stranger it will feel like.
Warning about making unusual games
The more you alter the 3Cs and verbs for your aliens, the less any human will be able to play -and worse, enjoy- these games. The harder it will also be to understand the game from an outsider point of view. If your world intention is not to put your audience at a state of confusion, bewilderment or unease, be careful not to overdo it and focus on a few core mechanics to make the learning and understanding as smooth as possible.
1 : There's one study that made a clear categorization of action verbs, alas I can't find it back 😞. In game design it was too abstract to be used meaningfully, though here it would have been very useful...