AUntil the end Maddox always clings to his principle of never drawing first. His face assumes a sad expression - each time a gunfight is forced upon him. The only time his faces looks vengeful is when he shoots Price in the back. Why is that?
Until the end Maddox does not know, what kind of man his rival is. Probably assuming his rival to be someone "better" than him. Only in the end he realizes that the woman of his dreams has left him in favor of a coward. This seems to hurt his feelings so much, that he breaks his rules.
Being a deeply emotional man (as is implied by his making music before), he takes revenge by "making her a widow". After the killing he rides intentionally close past by her, demonstrating that she is now invisible for him.
His harsh action may seem injustified, but one should remember that he has been villified throughout his life - and now the only girl he ever wanted has sided with the mob.It could also be construed, that the killing demonstrates Maddox' true nature of an evil murderer, but this is not very likely as it would negate the entire previous plot.