Now, I read the sentence ...
... "Traditional analysis of "competing" languages points to the eventual extinction of one, as was pretty much the case with ... Welsh and English," to suggest that Welsh had made English extinct. I admit that, come closing time, it seems that it might be the case what with all the spitting and slavering and hacking and slurring, but English is still most definitely the spoken language here.
Regarding Welsh as an extinct language - my wife and I have different opinions. She comes from a country which is very proud of the fact that they use a language that was basically invented by nationalists in the late 19th Century (i.e. Czech)*, and thinks that anyone should be able to speak any language they like, and have it recognised. On the other hand, I don't see the point of having made-up languages whether or not they have some basis in a language that people once spoke, particularly since they all seem to involve a lot of spitting and tongue-cramping noises.
* Czech, like Welsh, was a series of dialects spoken in different areas, and rarely written down. In order to make a language that could function as a badge of membership of a particular group, a written, standardised form was deliberately created (rather than evolved, like English, Spanish, and German, but not French which has conscious interference from language police), and is seriously compromised. Czech deliberately has strange letters (such as "ř", which represents "rzh", where the "zh" is like the "s" in "pleasure", even though they have two letters - "r" and "ž" - which would make the same sound. Even using the diacritic over certain letters was basically so people could look at it and differentiate it from other similar languages, which make the same sounds with different spellings (such as Polish). If you ever want to start a vigorous argument amongst Czechs simply suggest that they might have been better keeping German as their language after the fall of the Austro-Hungarian Empire, since they would then be less isolated from the rest of Europe. It is amazing how many will agree!