They're responsible for whatever user monitoring their third-party ecommerce platform does, right? All the ones I've seen process and retain user data. And maybe their web analytics, A/B testing, email newsletter tracking, etc.
If your point is that static brochureware sites that don't target EU members at all and don't do anything interesting on the web probably don't have much to worry about... then I agree, but I don't think that's very insightful.
Your earlier comment said that GDPR required "at least some active targeting of EU users." But a less contrived example, say a US-based SaaS that accepts credit card payments, probably needs to be very worried about GDPR even with absolutely no active targeting of EU users.