They have a very finite amount of new articles a day and a little box on the page with personalized headlines. All these articles, in fact all the articles on BBC of all time ever, comfortably fit into ram if you are so inclined.
Those little linodes have fast enough SSDs, try playing around and use one of countless stress loaders to get a feel.
I've served hundreds of thousands of requests a second from a single server using Varnish. A well tuned beefy VPS would do tens of thousands.
How to "personalize"?
For example Varnish has this thing: https://en.wikipedia.org/wiki/Edge_Side_Includes https://varnish-cache.org/docs/6.0/reference/vcl.html
It will happily read whatever cookie you set and stitch together a remixed personalized page for all the BBC users in the world without a performance penalty much faster than your lambda cold starts.
CDNs sometimes let you hook into Varnish directly or expose something similar to essentially do exactly this.
The aim of the game of the guy who wrote that blog post is to reinvent something from the 90s, but worse, and blog about it.