Most payers are required to mail their 1099's out by January 31. You may still get one in the next few days. If you don't receive one you are expecting soon after January 31, contact the payer and tell them you didn't receive one. Or do they by any chance post 1099's in your account online?
NOTE: If that January 31 deadline comes and goes, and you didn't receive it by early February, you should really try to get it from Twitch, since you'll need the EIN, and if it's a 1099-MISC, for instance, you'll need to know in "what Box number" they are reporting the income. i.e., whether they classify your income as royalties, non-employee compensation (self-employed), etc.
You have to report all income whether you ultimately get the 1099 or not. But you should wait longer and try to get it to know exactly how to report it.
I edited the above comments and included some additional info. If you were emailed the original answer, please return to the forum to see the full info.