For everyone interested, there is some info here:
TL;DR:
- When selling to the EU, the seller needs to pay VAT in the buyer's country
- MOSS is a system where sellers can report and pay their taxes for all EU countries at once, instead of each one individually
- For MOSS, the seller needs to provide two pieces of evidence showing where the buyer is located
- If the seller receives a direct payment (i.e. itch.io is *not* collecting the payment first), itch.io instead collects the buyer's IP address and billing address as pieces of evidence. The seller can then download that data in bulk to pay their VAT with MOSS
That doesn't answer all of OP's questions, but it helped me understand enough about what was going on. At the very least, linking to those existing creator docs in addition to the EU website would be a lot less puzzling than only a reference to ten year old regulations with a broken link.