When two pilots are required for a private aircraft, is it a requirement for the PIC to be ATPL?
Negative.  A person holding a private pilot certificate (at least in the USA) is allowed to add a type rating granting both PIC and SIC privileges in an aircraft type certified for a two person flight crew provided the flights are not carrying passengers or property for compensation or hire.  See 14 CFR 61.117.

An ATPL would be required if said type rated pilot was conducting Part 121 or Part 135 operations in such an aircraft.