Song lyrics are poetry. Often they don't make sense. It is common for a lyricist to distort the language to fit the meter and the rhyme. (The meter is the rhythmic pattern. In a song, the words have to fit the music).
Writing a song lyric is a little like working a crossword puzzle. A perfect lyric should sound like ordinary, natural speech, that just magically and effortlessly happens to rhyme.
Yes, here he is talking about "courage" as if it were "a sport" like football or basketball. No, that doesn't quite make sense. The idea, though, is that he doesn't take virtue seriously. He is acting as if choosing good or evil were just a game. His whole attitude is ironic.
Obviously the lyricist chose "sport" to rhyme with "rigor mort." But "sport" doesn't make much sense here. "Rigor mort" is a nonstandard shortening of the medical phrase "rigor mortis," the stiffening of the body after death. This also shows an ironic sense of humor. "Rigor mortis" is a frightening and depressing phrase. He actually is giving it a joking nickname.
"Purity" here means obeying society's rules about sex and romance.
A "yen" can mean a wish, a desire, or a yearning. "I have a yen for a pizza right now." However, "yen" sometimes suggests romantic desire. Therefore, the idea of purity itself being "a yen" is ironic. It means a desire not to have romances.
He goes on to say that purity is "very restful now and then." So we know that the speaker normally has many romantic encounters. He has so many they are tiring and exhausting. He is impure, he does not really want to be pure, but now and then he needs a rest.
By the way, "the seven deadly virtues" is a nasty joke, too. In medieval Western tradition there are "seven deadly sins:" pride, greed, lust, envy, gluttony, anger, and sloth (laziness). The virtues, the good things, are not called "deadly." So the speaker--who, I find, is the villain, Mordred--is turning everything upside down: good is bad, bad is good.