That answer presupposes that the seller's activity is such that it requires the seller to obtain such a permit etc. It is important for any seller to know the rules for their own state.
For my state (New Jersey), Atomic Avenue clearly meets the definition of a Marketplace Facilitator and it is therefore Atomic Avenue's responsibility to register with the state and to pay any sales tax that is due to NJ.
Remote sellers who sell to NJ customers only need to collect NJ sales tax if they meet certain thresholds, but this does not apply to marketplace sellers. The current NJ law "requires the marketplace facilitator to collect and remit Sales Tax on all marketplace transactions. The marketplace is required to collect and remit tax, regardless of whether the marketplace seller is above or below either of the economic thresholds."
If I make a sale on AA to a customer outside of NJ, then no NJ sales tax is due (page 8 of this document: "Items that are normally taxable when sold and delivered to a New Jersey location are generally not subject to New Jersey Sales Tax when they are shipped to a destination outside this State.").
So in my case, my understanding of the public NJ Division of Taxation documents is the following: (1) NJ sales tax only matters for my AA transactions if I sell to another NJ address, *and* (2) it is Atomic Avenue's responsibility to collect tax for those transactions and remit them to the state of NJ.
Other states (and in some cases, even specific municipalities) will have their own rules, certainly. Find them, learn them, and proceed accordingly.
Good rule of thumb: *always* report your income from all sources at tax time! 🙂