How can I gain practical experience in these things? The jobs I've had mainly revolve around adding new features, not doing any of the things described in the article. Does working at bigger companies actually give you experience with this?
Alternatively you could be the tech person in a 2 man startup that lucks onto success and grab onto your seat in a wild ride and just never let go.
The default/common path is evolving into the architect role which seems like a "bad" process of developing an architect.
The best way to develop a new architect, is to have him learn alongside a mentor/teacher who is an architect himself. Developing and architecture are very different jobs which require different mindsets and skills. Also, I've seen many places, teams, etc where people are mostly made to implement feature after feature with no time in between for learning, self-development, courses, etc.
Otherwise, after you've just "arrived" to that architect role you start learning on your own what architecture really is and means.
If you can find someone who needs something for their business or organization, you'll learn a lot of this by working backwards from what they need and building it. So I would suggest the opposite: the smaller the organization the more you can jump around and set up the basics of all these things.