Here is the way I (not the GP) would make the case: at the time HTML was invented, we had e-mail, chat, bulletin boards, ftp sites, and news groups. You could download pictures and movies and music (although the bandwidth and processing demands were prohibitive, especially for movies). What we didn't have was any way to visualize this: oh look, someone said that, referring to this, which is visualized by a thumbnail, which takes me to this other thing when I click it. Once this happened, the value proposition finally became obvious to a large swath of the population.
I agree with what you say, but here's a crisper statement: that the web was the first internet service to exploit the usability gains of the graphical user interface.
(There were graphical Usenet clients, but most people used text-mode clients. Even if graphical email clients like Outlook were used by more people than text-mode ones, they weren't significantly better because email wasn't designed to make use of them.)