Many of the words mentioned I haven't heard of or just learned (such as "chav") but haven't heard anyone actually use. Some of them I have heard people use more often lately, such as ginger (though in my circle of friends I'd argue this has more to do with the South Park episode on them), bloody, Autumn, bum, cheers (especially to end email messages in the office), roundabout, shag, and twit. And then there are others listed in the two links that I have heard all my life, such as pop over, gobsmacked, and one-off. But are they really trying to claim the term "to go missing" is a Britishism? Seriously? That's a pretty basic and common phrase that I've always heard, I don't think it can be "claimed" by anybody.
And I know this wasn't meant to be a scientific study or anything, but I do question their methods in the article, such as using a Merriam-Webster dictionary to show which British words have been added. Anyone who browses through a dictionary knows that it includes tons of words that you would never hear on a daily basis, and possibly never hear in your lifetime. Not really a good judge of what's in popular usage. Also, some of the terms they mention are used in both places but are considered Britishisms because they date back over a hundred years...well if we're going back that far, really we should be considering everything a Britishism.
I do agree with the overall point of the article though - that more British terms are creeping over here. A few have become naturally integrated into our language, but I'd say that more often British terms are used to sound more pretentious or fancy, in a purposefully amusing or mocking way. Or, when I was a teenager, some of my friends started spelling words with added u's to sound smarter, such as colour, honour, etc. They thought this made them seem more sophisticated and "in the know" than their peers.