Burslem is one of the Six Towns of Stoke-on-Trent, so Port Vale are Everton to Stoke City’s Liverpool.
I know that this is the way that it’s done in Britain and elsewhere, but I also find it do weird, I’ll never be able to do it myself. I will personally always say **“Blackburn is …” **and **“The Rovers are …” **I hate it when American sports reporters affect the British style. Makes want to slap them.
This reminds me of “in the hospital” vs. “in hospital” – it is not so much that American English uses one form and British English uses the other. It is that British English uses both, with slightly different meanings. The singular is, in fact, sometimes used with sports team names in British English. For example the sentence “Arsenal is a football club in north London” sounds perfectly correct in British English. You could also use “are”, but in this context I would expect “is”.
In general, British English is open to the idea that an entity can be both plural and singular in nature, so that depending on context it can be appropriate to treat the respective noun as plural or singular.