Actually you have it backwards...Taekkyon started out as a martial art and became a folk game. As far as ssirum is concern, you would have to exclude all wrestling out of martial arts based on your view of Ssirum. For that matter, Kumdo, Judo as well since they are for sport not for "war".
While it is true that Koreans look towards more scholarly pursuits due to Neo-confucianism, martial arts were not looked down upon as so many would think. In fact many of the upper caste learned martial arts as part of their education and training.
Mooyedobotongji was based off of military arts which were basic instructions in weapon work and some unarmed combat. While you can credit the vast majority on Chinese arts there are some that are also Korean based as well.
True!! Wrestling itself is a form of Martial Art, Boxing too!
Actually if you know your history, you'll know that many Martial Art systems became sport thereafter in order to 'survive' during the occupations and years... It was a survival mode.