ATP is usually a requirement for a Chief Pilot or Director of Operations in Part 135 - as you can give training in 135 ops with an ATP certificate. (A CFI/I/ME would also do)
They may be advertising for a CP or DO, in which case you would need 3yrs experience as a CP or DO at a Part 135 or 121 operation within the last 6 yrs - I think this is in Part 119 or 135.
Isn't anything that isn't Transport Category considered light - ie BE1900, SA227 etc... - both require ATP for Captain