Let us not forget dancing...knights were required to be skilled in all of the courtly arts. I did not know archery was among them...considering it was looked upon as a commoner's weapon, I wonder at that.
I think they are all important, in their fashion...by learning each one, you expand not only your knowledge base but your conscience as well, as now you have something else in which to identify with; the courtly skills offset the martial ones. Orwell once said 'We sleep safe in our beds because rough men stand ready in the night to visit violence on those who would do us harm.' - those rough men, without any training in the finer arts, would always BE rough...and ready. Good for when they're soldiers, bad for civilian life.
Riding, swimming, fencing, falconry, hunting, wrestling - these are the physical pursuits that hone your skills for combat, make you into the warrior you've chosen to be. Chess, poetry, music, dance, courtly love- these are the pursuits of the mind (and heart) to remind you of why you do what you do- you protect these institutions because they remind you that you are human, a thinking man as well as a fighting man...a person worth being around, knowing, etc. A man who has only the martial element will always be needed, but often misunderstood- and once his service is complete, forgotten.
That last sentence resonates with me...it is what I see occurring all the time with regard to our armed forces. The media uses words to buffer the horrors these men and women face, they refer to them as 'troops' rather than soldiers or people to lessen the impact- they are different because they've set themselves before our enemies to protect us, but instead of exalting them, they do the opposite.
I'll end with- I think all of them are useful skills- a knight should be well versed in most, if not all, if he wishes to be successful not only on the battlefield but at court as well, where those other skills would've been put to good use.