Yes actualy if you read the rest of his abilities he gets all these other feats for free even without qualifying for them I would think they meant that ability with mobility to operate like that as well I dunno anyone else?
The emissary archetype grants mobility:
"At 5th level, an emissary learns to be more aware of the threats that surround him in combat, and shares this awareness with his loyal steed. Both the emissary and his mount gain Mobility as a bonus feat.
This ability replaces banner."
Does this mean a cav gets mobility even if he does not have dodge?
I will say yes. Typically bonus feats awarded as class features ignore prereqs. Look at ranger Combat Styles for another example.