So you haven't read all the article, or at least, engaged with any of its points -- perhaps rolling your eyes forwards may help in the future.
The claim the author makes is that British English will die as a distinctive sort, being subsumed by foreign additions that make little sense to the way we live our lives.
"After all, as a nation we’ve been both invaded and invader, and our language is all the richer for it. Words like bungalow, bazaar, even Blighty, have their roots elsewhere. Heck, go far enough back and isn’t it pretty much all just distorted Latin, French or German?"
Not really, it goes mostly from the direction of the stronger nations to the less strong in the relationship.
And cultures and languages do die out in such processes.
Now, some might find all this inconsequential, but for some of us those things means something (and the fact that historically things change and die anyway isn't more comforting than it is when its told about one's family dying).
What I'm more amazed is how people can lament some latest sequel to a movie franchise "betraying" or losing the spirit of the original or losing its way etc, but at the same time can't understand others that are concerned with whole cultures doing the same.
Well, isn't that a strawman too? Seeing that, I didn't say those are "necessarily" the same people -- just that "some people" hold both opinions simultaneously.
As an American, I've noticed certain words I associate with British English creeping into our vocabulary as well. In my mind I associate it with Harry Potter and Doctor Who, but I realize Anglophilia is no new thing--these are just the bits of British pop culture that hit me in my early adulthood.
The fact is that British and American English will each remain distinctive, even as they continue to share and evolve together as well. The Internet is definitely making this evolution happen more quickly. But it still goes both ways, and will continue to do so. Some of the changes you'll like and adopt without thinking about, some you will find annoying or crude, some you will hate with a completely irrational passion. It's part of life. Enjoy it!