Not correct

I hope this is just another case of media messing with the facts - not some ill-informed master doing the same.
Without a doubt taekwondo and karate are the two largest martial arts worldwide. But to claim that these are the only two martial arts to be practised "all over the world" is a pretty bold statement!
I would strongly suggest the same goes for (at least) judo, kung-fu/wushu, tai chi, aikido and jujutsu.
Anyhow, at least this article states the truth about the age of taekwondo, not the "2000 years old" hype.

Story:
Although the history of taekwondo is sketchy at best, Koreans generally credit General Choi Hong-hi as one of the earliest pioneers of the sport. In 1954, Hong-hi required the Korean army to train in Taekwondo, meaning the very first Taekwondo students were Korean soldiers. Coupling a heavy influence from the Japanese, the actual martial art known as taekwondo was developed between 1945 and 1955 and only became known as Taekwondo in 1955.

Nowadays, taekwondo is one of only two martial arts systems (the other being karate-do) to be practiced all over the world, boasting an international membership in the millions combining over 140 countries — making it the most practiced martial art style in the world.

Source