My blog is not even three months old, but I definitely view it as a business. I enjoy writing and running the website, but I would not be putting all the time into the site if I didn't plan on one day making money from it.
When I was in college I got paid a couple hundred a month to do marketing, SEO, social media, and other ad-hoc work for DINKs Finance. I learned a lot about running a blog as a business from the owner, James. They treated the site as a business very early on and I hope to follow their model.
I am trying to be very intentional about planning where I want to go with my site. My first goal was just to get the site up and tweak a theme myself (despite almost no coding experience) to look decent. I got that done. Now I'm building content and connections. Next I plan a site redesign. Down the road I would love to have 3+ posts a day with multiple hired writers contributing. Most important is patience for me right now and taking it one step at a time.
That was kind of a long answer to your relatively simple question, but yes, I view it as a business.