>Why on earth would a cryptocurrency-based store have to comply with the same regulations as a card payment processor?
Because money laundering can happen at any level, and specific regulations apply, you don't need to be a card payment processor processing "payments for vast amounts of third parties".
As long as you accept payments, even for a lemonade stand in the corner, you need to comply with these.
In fact you probably misunderstood what Stripe demanded on the parent's situation: they didn't demanded the parent's store comply with the same regulations Stripe does as a card payment processor. They demanded they comply with the regulations a store should comply with.
One is just accepting payments, the other is processing them for vast amounts of third parties.