Actually, Trooping the Colour is broadcast live in several countries, and others show delayed highlights. I believe that Germany is one of the countries where it's shown live.
There is a unique bond between the Anglo-sphere countries which is hard to explain. The family ties are so deep that a lot of people here don't look at people from Australia, NZ or Canada as 'foreigners', but as kind of distant cousins (whom we like to beat at sporting events
). You'll struggle to find a family in the UK that doesn't have a family link to those countries. The link is probably not so deep with the US, but even even there estimates suggest that up to a quarter of Americans have some British ancestry. In the 1980 US census, over 32% of Americans claimed British ancestry, which would be the biggest single ethnic group in the US.
There's also the fact that after their neighbours in Canada and Mexico, the UK is the most popular destination for Americans travelling abroad. QEII has an approval rating of over 80% among citizens of the US. She, Charles, William, Kate and Harry would be quite well-known there.
All of this, I think, fosters a certain curiosity which goes both ways. The lack of a language barrier makes that curiosity fairly easy to satisfy.
What I don't understand is countries with their own monarchies being interested in ours. I mean, Denmark, Sweden, Norway, the Netherlands, Spain etc. all showed William and Kate's wedding live from what I remember. All have had their own big royal weddings, wouldn't that make them much less interested in another monarchy's activities than republics who don't have their own royal occasions?