Does having a website make you an influencer?

I think the problem with the word "influencer" and the cultural baggage it now holds within the Internet is that it's specific to that kind of person solely on social media who chases/makes trends in exchange for popularity. It's properly the word "influencer" that doesn't collide with the web revival world because it sounds like a poor lexical choice, doesn't exactly describe what uhm, "famous people with personal pages" do.

If anything, maybe "inspirer" could be a more fitting term. I've always seen people with "famous" personal websites trying to give something in return to the community they managed to grow around them: way back then it was oekaki boards, templates, buttons for your Livejournal; now it's forums or Discord chats, resources, (new) webrings, code suggestions.
I haven't been "influenced" by my favourite webmasters because I haven't followed them blindly; rather, I made lessons learned on their websites/about their websites my own and grown from them.

So yeah, to also respond to the first question: influencer and webmaster are two separate roles on the net.

(With that said, I can imagine someone could be -both- an influencer and a webmaster, if they wanted...)