Articles misses that this is in response to SF's gross receipts tax. Payment processing is an ultra low margin business, no way they can compete while paying ~1% of revenues to the city.
I believe it is gross receipts within the City. The impact is surely negligible
The item specifically relevant to Stripe is that it's categorized as a Financial Services rather than Information company. Financial Services companies have to allocate gross receipts based 50% on their payroll location and 50% based on their sales location. So while their portion of sales in San Francisco is negligible, most of their payroll is there.