No, they don't need to register all domains with xenforo, as that would be impossible and it would be cheaper to register your name globally.
Mike or Kier could certainly state whether they have lodged the documents or not, but basically even though you put TM onto a domain name, it means nothing outside your physical location, ie. they are a UK company, so they could challenge trademark of xenforo against any new UK based company, but not International. Also, trademark only applies to the industry, ie. software, which when trademarking can come with support, faq, modifications, styles... you can add relevant sectors which will encompass many other things. That doesn't stop you starting up your own xenforo sprinkler company and then trademarking xenforo for use on sprinklers. That stops someone else using the xenforo brand name on something within the plumbing / sprinkler industry.
® is for an officially registered trademark within the country, ie. Pepsi, Coca Cola, big companies, register in every country they sell within or plan to sell within, thus ceasing any use of their brand name in pretty much nearly anything, industry related or not... but that costs massive dollars to achieve, of which would normally bankrupt a small to medium size business.
Trademark and even business names are country specific unless specifically registered across International borders. Just because the Internet is global, if you reside physically in the US as an example, and xenforo is not registered in the US as a trademark, then you can use xenforo, even in direct competition under xenforo the company you register in the US... different countries. Existing companies have held up the biggest of global companies with trademark use... just look at Burger King in Australia, hence why its called Hungry Jacks and branded uniquely, as a little business in NSW had the name Burger King registered before the US giant came here, and they couldn't do a thing about it and stopped them from using the name Australia wide for a long time until they finally bought it out. Only in the last few years have they slowly been swapping out Hungry Jacks to Burger King.
Location, location, location... and because you can reach any border via the web, doesn't negate location laws.