you can walk from korea to portugal and to south africa. "continents" are just an out-dated artificial construct and only important for those that need to label things. Australia used to be a continent, then it was Australasia, and now its Oceania - even though under any of those defintions, you cannot walk between all places.
Also, Antarctica is definitely a continent not part of the olympic rings.
But you are also correct, it is primarily an english-speaking problem, because for over 200 years people from the USA have called themselves American. I guess we have to respect that? As long as they don't start re-naming things that dont belong to them ....