Q: Who decides what camping activities qualify for the camping requirement needed for election to the Order of the Arrow?
A: With the camping requirement, as with all other eligibility requirements, it is the unit leader's job to interpret whether a Scout has met the requirement.
As stated in the Guide for Officers and Advisers (#34997A, 2012 revision, page 20):
"Unit Leader Approval. To become eligible for election, a Boy Scout or Varsity Scout must be registered with the Boy Scouts of America and have the approval of his unit leader prior to the election. The unit leader must certify his Scout spirit (i.e. his adherence to the Scout Oath and Law and active participation in unit activities). The unit leader must also certify that the nominee meets all specified requirements at the time of this annual election."
Other than defining the length of time needed for a camping activity to be considered a long-term camp*, the National Order of the Arrow Committee leaves the interpretation of the camping requirement to the unit leader.
* A "long-term camp" is one consisting of at least six consecutive days and five nights of resident camping. A "short-term camp" is anything less than that.