"This one-time bonus offer is only valid for first-time United MileagePlus Explorer Card members with new accounts. Previous and existing United Airlines cardmembers/accounts are not eligible for this bonus offer."

I am reading this as any MileagePlus Explorer account (Visa or Mastercard), which I assume your continental has now converted to. But whether this is put in practice or not, I dont know. Other posters in this forum have had success getting the bonus even though they hold non-explorer United cards, which is in contradiction to the second sentence of the above terms and conditions.