Not gonna lie, I confused this site for one of those sites you see on parked domains. I can see a resemblance with respect to the color scheme, but I think the entire design aesthetic is completely different.
I had the same impression (on an iPhone). I'm not really sure what contributed to my unconscious snap judgement, but I think it has to do with the layout of the search box and list of links, along with the lack of images (other than a little icon in the corner) and the four copies of the domain name (in all caps) on the page.
Arguably unifying of back-ends are more important than the visual design for consistency and ease of use though.
The introduction to the article shows several different styles of registration or login button used across different US govt departments, but the key point here is that they're all separate user identities requiring separate logins. Making visually identical login flows that actually require different credentials to log into separate services actually makes things worse for periodic users of multiple government sites. What's needed as an even higher priority than changing the buttons is a uniform OpenGovernmentID everywhere it makes sense to do so
Priority number two for ease of use in government websites would probably be fixing link rot, since government websites have a horrible tendency to deep link to other departments just before that department's site gets reorganised or renames (and departments whose sites were replaced by the gov.uk platform unfortunately are no exception)
That article is bullshit. You can't judge gov.uk by its homepage, because that's almost never where you land.
Now that we have gov.uk, whenever I google something about doing my tax, or registering to vote at a new address, or any other arduous governmental admin shit, I usually end up on a beautifully simple and focused gov.uk page, and I'm in and out in 2 minutes. That's what a government website is about.
Look at how brief and clear the writing is. Look at how straightforward its URL is. Have a look at some more pages, look how consistent the design language is. This is exactly what a government website should be like.