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It would be classified as income, yes. And you’d get a 1099-K from Stripe, who is taking the payments. Depending on how you file taxes, it would either be considered personal income (and you would file the forms to offset that as a self-employed individual) or you would include it as business income if you have a Corporation or LLC.
From their site: https://www.kickstarter.com/help/taxes
Creators who have passed over the thresholds established by the IRS (currently $20,000 in gross volume per year and 200 or more transactions) will receive a form 1099-K from our payment processor, Stripe, in January following the year in which their project was successfully funded.