It's a little spun, I think. Clearly there were earlier computers (like ENIAC and Colossus, which the article mentions) that also pioneered critical innovations. Equally clearly, there were many more inventions to come. The article seems to pick out "program stored in volatile memory" (ENIAC, at least, was hand-programmed offline. I'm not sure about Colossus) as the defining characteristic of the "modern computer".
Meh. I might argue that CMOS VLSI process technology was actually more important, being the biggest "hard part" of figuring out how to manufacture the actual computers we use in modernity. But whatever, everyone has their own favorites I'm sure: do we all get to write articles for the BBC?
Last weekened I visited my aunt who lives round the corner from the Museum of Science and Industry in Manchetster - it's well worth a visit if you're in the area.
http://www.msim.org.uk/
Definitely a landmark achievement for humanity, but hardly a "personal computer".