Selling to Saudi Arabians and selling to Saudi Arabia are two entirely different things. In one you're doing conducting business in the Saudi Arabian market, and therefore under the umbrella of their government and in the other you're conducting business in whatever market the person you're selling your alcohol is located at, and under the umbrella of that market's laws.
When an EU business buys a service from an American operating in America from their website hosted in America how is this materially different than when a Saudi Arabian citizen visits New York and buys alcohol?
Because the EU business is not located in New York. It's located in the EU. By providing a service to an EU resident you are interacting across the US<->EU border and thus EU laws restrict what services you can provide across that border. I would recommend thinking about it like shipping products overseas.
