The first and second parts of this archetype are diametrically opposed:
"a master of many styles may select a bonus style feat"
Dragon Roar IS a style feat.
"He does not have to meet the prerequisites of that feat"
One would assume this includes having the prerequisite style.
"Alternatively"
Or you can
"choose a feat in that style’s feat path... if he already has the appropriate style feat"
This is not well written.