It appears Etix licenses their platform kinda like Shopify does, but also uses it to power their own marketplace. It seems Louis CK is licensing it. It kinda make sense to use the software that's already been built rather than creating a custom solution, and I imagine this is something that seemed to work for him (or whoever manages his website).

I'm not sure how you expect to pay by credit card without using a payment processing gateway. Even if you paid by cash, the post office would be a middleman as you'd have to pay postage.

I assume by "cutting out the middleman" they mean the ticketing cartel otherwise known as Ticketmaster.