So long as your Twitch income exceeds your Twitch-related expenses, you will have extra income and a corresponding tax liability.
A hobby is entered as Mike9241 describes above. However, Twitch as a business is entered on Schedule C.
The good news about making it a business is you can better deduct your expenses, even to the point of showing a loss; the bad news is that you will owe self-employment taxes (if you show a profit).
So the question is, are you just goofing around, or is this going to grow into something at which you intend to make a profit?
Please see the following that I wrote last year about my thoughts on Twitch streaming as a business:
A "streamer" is a person who creates content that is streamed on the Twitch platform. This content can take a variety of forms, but is focused primarily on gaming (does this mean that a lot of the content is streamed online video games, where subscribers watch well-known gamers play?).
***Note for the rest of the audience - see this article on how to make a living being a streamer which describes how streamers monetize their content.***
Now that it is clear that you can make money from being a streamer, the salient tax question is, "are you doing this with the intent of making a profit?" That is, are you doing this as a hobby where you might (incidentally) make money or are you doing this with the intent to make a profit (i.e., a "business")?
If you are doing this with the intention of making a profit (like Destiny in the above link), then this is clearly a business, which would be reported on Schedule C (assuming that you are not a partnership or corporation). Any income that you receive would be income to the business and any legitimate business expenses would be deductible. The IRS says that to be deductible, a business expense must be both ordinary and necessary. Obviously, what is ordinary and necessary varies wildly between industries.
With this understanding, let's look at some common terminology:
Donations are money given indirectly (using an in-site currency known as "Bits", purchased through Amazon Payments) to a channel. A "partner channel" is under "the Partner Program (which) allows popular content producers to share in the advertisement revenue generated from their streams. Additionally, Twitch users can subscribe to partnered streamers' channels for US$4.99 a month, often granting the user access to unique emoticons, live chat privileges, and other various perks. Twitch retains US$2.49 of every US$4.99 channel subscription, with the remaining US$2.50 going directly to the partnered streamer." (from Wikipedia). The partner (i.e. the content creator or streamer) gets some or all of the "donations".
It appears to me that "donations" are like tips to a waiter or concierge, voluntary contributions to a service provider. In this case, the streamer (Partner) reports the "donations" as ordinary income on Schedule C. The donor, however, cannot take this as a contribution, because contributions are deductible ONLY when they are given to an IRS-recognized charity.
As for the "networking”, I am wondering if this is a euphemism for advertising expenses or other money paid to increase your content's exposure and salability. If so, then the so-called "networking expenses" would be deductible as an "ordinary and necessary" business expense on Schedule C for the partner streamer. (Apparently there are also other classes of streamers like "affiliates" who might also legitimately claim that their activity is a for-profit business).
NOTE: for users of Twitch, there are no deductible expenses, any more than you can deduct buying comic books or music videos. The comments above are primarily for people engaged in the business of generating and delivering content through Twitch.
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