Is it mandatory to officially register a company or bussiness to sell a game in any global platfrom like Steam? LEts say that a couple of friends createa game and decide to sell it under the name of The Two Guys Game Studio. Should they register a bussiness under that name to be allowed to sell?

Depends heavily on laws in your country (and regulations imposed by the platform - like Steam).

In my country (Czech Republic) I'm allowed to sell anything as private person, if the sale results non-regular income. Any regular sales that results in income must be a registered business. Under this category you could fall if you F.e. sold your game only as part of some event. For each sale done like this, a standard buyer-seller form has to be filled in.

Any regular income has to go through business, and here you have many options - the most common:

• “Tradesman” or “Sole proprietor” is the smallest business unit you can register. It is always owned by 1 private person. It can do ANY business activities (can employ other people, can be VAT payer, etc.) and it has to satisfy all legal requirements (mainly taxes and properly filling bureaucratic forms, the advantage is that it can use simplified accounting)
• Company with limited liability (it is a similar equivalent of LLC - called. “s.r.o.” here), although not really being an LLC (due to laws here). Legally it is a company owned by 1 or more subjects (can be either private person or other company), where each has percentage of the ownership defined in agreements (signed by owners, and created/updated by notary).
• Stock company (or “a.s.” here), which can be owned by 1 or more subjects, but ownership is defined by the amount of stock company released. It can be publicly traded, privately traded - or technically anything in between.

Each of those does exist in more or less similar form in almost every country in the world (and if you are living in one of those where private businesses doesn't, I'd recommend you to run away asap - as it is not going to end well). Any of the 3 above will be fine for everything related to regular sales (like selling games through digital platform) - all receive their own Tax ID number ("ICO" here) and they may also receive VAT ID number ("DIC" here - you will need to provide this one if you're company in EU member state).

Selecting a proper one is harder though - if you're a single person, the first option makes the most sense (as long as you don't want to do that much accounting - which applies here, but some countries may still require you to do). For multiple people, doing LLC or equivalent makes the most sense (there is percentage of ownership for everyone - which then clarifies how revenues are split), doing stock company most likely doesn't have much sense unless you want to enter stock market with that company.

Keep in mind you can switch F.e. from LLC to Stock Company, it is possible and it happens (requires a TON of bureaucracy here). Even vice versa (although that is more rare).

In the US you can do business using a DBA (Doing Business As) name. This is the same as being a sole proprietor, but you get to pick a name. DBA names usually have to be registered with the local county. It's easy to do. Doesn't change your tax status. You can often open a bank account with your DBA name as a business name, which means you can cash and write checks in that name. You can get FedEx and UPS accounts with your business name, so you can ship stuff. You can register domains. So you can act like business.

In addition to other companies like Steam doing business with you, there are concerns about ownership, distribution of payments, and more.

At the very least a written collaboration agreement is needed. Rights assignment is more typical, so that a single entity owns the product. Without the agreements then everything done with the game at Two Guys Game Studio is owned individually by each of the two people. If someone dies, loses interest, or decides to not participate, they can block anything dealing with the game. The One Guy who remains can't even make a derivative work to replace Other Guy's work without legal encumbrance.

Written documents about how payment should be handled are also recommended. The best for hobby development is to make all payments discretionary. The best for a business is regular employment with a specified wage, or contracts which have clear starting and ending terms. If it must be divided under a percentage, then if someone came in with money ten years down the road whoever took the money would still be required to track everyone down and give them their portion. You can specify the intention, that a percentage distribution of profits sent to people, but good agreements will specify what point is not enough to bother, and define what amount needs to be distributed versus what should be retained by the studio.

Termination is important in the documents, how rights and responsibilities are terminated. There are some difficult stories of contract workers where the company didn't follow the procedures sent in the agreements but instead just slowly ghosted the individual who felt they were still working under contract. When payment time came along, and the business felt they weren't a contractor any more and shouldn't get paid, the fallout was pretty severe. In one case I know, the company basically went silent, replied to messages with emojis rather than a clear statement like “I believe the contract ended your employment on February 30th, is there something more you needed to discuss?” In that case the lawsuit fell out badly against the company because they tried to ghost them, and they ended up needing to pay about 750K.

It is an area where you really need a competent lawyer to help you out. Employment law and unemployment insurance, taxes (governments are picky about that and can jail you over it), IP ownership, terms of service, and so many other legal hoops must be jumped through. Getting it done correctly can cost a few hundred dollars if you know what you're doing, a few thousand dollars if a lawyer needs to do it for you. … But getting it done incorrectly can bankrupt you if things go bad, so if you can't afford to do it right you probably can't afford to be doing business.