In principal. A private arrangement not being made availible to the public (In this case only) or being advertised, and flown by an appropriatly qualified and skilled pilot for hire and reward. This answer is given specifically in reponse to what you have posted and should not be construed as to apply to any other circumstance. You really need to have intimate knowledge of the regs.
In my your situation is in effect being employed and paid as if you were a corporate pilot employed by the company which is conducting private operations as is the case with several corporate jets. You would need to check as to whether or not the aircraft is registered in private and or airwork catagory and obtain advice as to whether or not it needs to be airwork. I suspect corporate aircraft may be registered in airwork albeit the flying is done as a private flight.
[ 29 November 2001: Message edited by: rpt2 ]