Very funny that you brought up a band as an example-- when I read your questions that's exactly the example I was going to use...
No, you do not have to form a separate legal organization. There are benefits to doing so, but it is not required.
Regarding the money.. Assuming there is no separate legal organization, then someone (one of you) will be the one to whom the checks are actually made out or whose bank account the money is deposited. And someone (one of you) will have to provide your SS number to whatever you are using to collect money (beit paypal, Apple, Steam, etc.). So that means that one of you will have to report the game income on your taxes. This will, of course, increase the amount of taxes that you (personally) need to pay. So to deal with that, you have to make sure that you write checks to the other members of the team for 'their share'. And then, come tax time, you may need to tell the IRS "Hey, I paid some people who worked on the game, so don't tax me on that." You will (unfortunately!) become quite familiar with "Schedule C" and "1099's".
That's actually very much like how a band works as well. Someone got the gig, and the check is paid to them, then they turn around and pay the band members.
Yea, it's a bit of a hassle, but that's generally how its done. Good recordkeeping is essential. It's for this reason that, even if there is no separate legal entity, most people set up a separate bank account only for the 'business'.
It is by far preferable to have an agreement written up well beforehand to explicitly state ownership and money expectations. You're correct that often that doesn't happen until 'later', but that is really just asking for trouble. As with a band, once real money is on the table, all the "unsaid" assumptions get challenged and things can get nasty quickly. Far better to agree before there's anything really at stake.
You don't necessarily need a fancy contract (though it's certainly best). A simple plain English document explicitly spelling out what you all believe the arrangement to be (and then signed by everyone) is certainly far better than a verbal agreement or unsaid assumptions.