So I don’t think the argument is “is a designer an artist.” I think the article discusses more “is a designer a fine-artist.” And the answer is, it depends.
“In European academic traditions, fine-art is art developed primarily for aesthetics or beauty, distinguishing it from decorative art or applied art, which also has to serve some practical function” (Wikipedia).
The article pointed out that designers work for other people’s wants and needs. Designers take a problem, analyze it, and come up with a proposal. Fine artists have more freedom to create what they want.
So design can be a “fine art” if the designer has freedom and is able to use their imagination and create something imaginative, beautiful, and intellectually stimulating, then it can be considered, per definition standards, a fine art. But if the designer is restricted in imagination and is only serving the purpose for advertisement to get people to buy a certain product, then I personally don’t consider it a fine art. It could be considered “art,” but not fine art. More like functional art.
So really it depends on the situation you are placed in, and what kind of ‘designing’ you are doing. Are you designing something aesthetically beautiful that engages the viewer and makes them think about life? Or are you designing a product that is for functional purposes only?
Fundamentals of Communication Design 