You are the owner if the game if the game's art, music, code, etc; is rightfully given or created by you or someone else. I do not know what you mean by "This is a collective or partnership, but not a registered business", but there is two ways i know to say this legally.
- You are either in a temporary partnership or in a partnership with the person.
- You are the sole proprietorship and you hired someone.
Partnership and Sole proprietorship are two different things. Sole proprietorship is only you the person who the IRS will talk to you while Partnership is two or more people the IRS wants to talk.