What are the requirements for game designing?

Game design is one of those sort of amorphous fields that doesn't really have hard requirements to get into. There are however a lot of skills and experiences that can help you become a better game designer.

1) Be skilled at communication, especially written communication. Anyone can be an "ideas guy", but it takes skill to take those ideas and break them down in such a way that your vision is communicated to the rest of the team. Designers are not islands, they must work closely with all the different disciplines (including other designers) that are coming together to create the game. One of the main things you will be doing as a designer is writing design documents, which depending on the scale of what you are designing for can be many many pages long.

2) Be a polymath (a person of wide-ranging knowledge or learning). Games as media range over a huge number of subjects. Because games are reflections of real world experiences, a game designer must have some knowledge of those experiences in order to make a compelling game. To a game designer, there is very little knowledge that could not be potentially relevant. History, biology, engineering, physics, art, music theory, psychology (especially psychology); you don't have to be an expert in every field, but working knowledge of a wide variety of topics can help you at least identify what you will need to explore in more depth. As a corollary to this, always do your research. This doesn't mean that you necessarily have to go to war in order to make a war game, but interviewing soldiers who have had that real world experience will help you find ways to bring depth to your game that you wouldn't have had otherwise. Knowledge is the birthplace of inspiration.

3) Play games like a designer. When playing games, examine the design decisions they made and how effective they are. If something is boring or frustrating about a game, try to identify what weaknesses in the design are contributing to your negative opinion. If you're spending hours playing it, step back and examine what about the game is drawing you in. Is it truly engaging, or is it stringing you along endlessly with reward loops? Play games not just for fun, but for studying. Play games you wouldn't normally play, genre's you aren't drawn to, kids games, "girly" games, casual games, browser games, tabletop and board games, right along with mainstream AAA. Too many new designers limit themselves to the games they like to play and can miss out on understanding huge portions of the market. After all, those market niches are there for a reason. I'd recommend watching this Extra Credits episode (part one and two) as they break down why this is important and how to do it much better than I can in a single paragraph. Actually I'd recommend watching that youtube channel in it's entirety. It's great thought material for aspiring and experienced game designers alike.

4) Take game design courses. It's true that you can be a very talented designer without ever having set foot in a game design program, but most reputable design courses will bring you through a lot of important topics that aren't really covered elsewhere or are only really relevant in the context of game design. Things like how to employ random elements without making the game luck based, design methodologies that simply wouldn't come up in any other area of study, research done about games and gamers, managing project scope, relevant psychological concepts like reward loops, flow, and creating illusions of choice.

5) Script. You don't need to be able to script in order to be a designer, but understanding code logic and how to make events happen within a game engine will make you much more valuable to potential employers. I'd really recommend doing some unity tutorials to get a handle on C# or use UDK to play with visual scripting and blueprint, which I believe is just C++. It will also allow you to make more games in a digital format and experiment with ideas without having to ask for outside help.

6) Make games and make lots of them. This is the most important thing you can do. Practice really does make perfect, and the more examples of good design you have on your portfolio the more you can convince people you know what you're doing. Your games don't have to be pretty, but they do have to be fun. A well designed game that uses only gray cubes is more valuable on your portfolio than a pretty game with awful design. When you're starting off, don't make the mistake of planning big open world RPG's or complex multi-player experiences. Your first few games should be small and simple, but polished. Branch out as well. Board games might seem like they're not relevant, but the skills are transferable and a published board game is a great portfolio piece.

Benjamin said all the right things and I can tell you that you will hear everything he said again, from various sources.

I'd like to add that #5 and #6 will have to be your #1 and #2 priorities. If you don't like to code, I don't think I can rightly advise you to pursue anything but making table-top board games. I don't know of a single game design job that accepts someone who can't code C# or C++. Without that, you're the dreaded wanna-be "idea guy", (unemployable).

If you want to get consistant work, or work at the AAA level you had better know Unreal, or know Unity if you're more indie inclined. There are so many game engines out there that are nothing like Unreal or Unity, but you have to get your feet wet somehow. I can't stress this enough. The field of game design has vastly fewer jobs than people think, and there is an army 10,000 strong and growing, full of young people that have good people skills and good ideas. So why would anyone not hire the code proficient and game engine savvy ones?

Benjamin also correctly suggested to play all manner of games. There are roughly 5 or 6 types of game designers out there ( Here are just two types: Types of Game Designers)
and they all benefit from exposure to the entire industry. And you need to understand games AND the industry before you have a job, kids, and never-ending errands. Because later in life you may have as little as 2 hours and maybe a whopping 12 hours of gaming per week to keep you from becoming an out-of-touch dinosaur.

In addition to what Benjamin said, you want to consider the title's budget, team size per dept, technologies that may have been created and how those innovations were impeding development (until the last few months before ship). You need to learn about pathing, AI, State Machines (google Fixed State Machines to start), a little bit about animations and collisions, and then start evaluating games on yet another level of awareness.

It wouldn't hurt to consider who is the developer and the publisher controlling the budget. Find any stories about teams being burnt out / game released early or late / studios closing?
Make time to read post-mortems from industry greats and indies. They are literally telling you the obstacles ahead of you, by explaining what they learned from what went wrong or right.

And for the type of game designer I most resemble, you need to understand why a game was made, who it was truly made for and how much money and time they got to make it compared to other titles. Consider how does the meta game design / monetization and game mechanics push people to spend more.

There is a basic requirement that you have to be HONEST, especially when you mess up or are going to be late. Lying and trying to run from accountability is almost a guaranteed dismissal, and asking for help when you really screw up is the best thing you can do.

You need to be pretty darn organized, spell korrektly, and have a vocabulary that is above-average. Don't use words you aren't 100% sure what they mean. Your grammar doesn't need to be perfect, but you MUST know the basics ( then/than, there/their/they're, it's/its, team's/teams' ).

Your ability to be empathetic when you critique others' work while also conveying compelling reasons why something needs to be reworked makes you very valuable. I'd attempt to convey information at or above my level, and you really should learn to be more concise than I am.... apparently.

Junior employees should rarely get snarky or fight back for your ideas because your lead simply just knows more than you and understands the game engine and marketing plan better than you. NEVER lose your temper (until you are a lead).

You are always courteous and never passive-aggressive to all the... "passionate" forum posts (your fans). And you can never, EVER play it loose with the security of data, taking the game build or data home without permission, breaking an NDA anonymously, speaking or complaining to reporters, or messing up a marketing campaign in any way. Because...?

You guessed it! Games need to be profitable! Yay!!!
(So the publisher doesn't lay us all off and close the studio... Yay!!!)