In your particular case, it doesn't matter, as the Sofitel Dubai isn't in the Fine Hotels and Resorts program. Your Platinum card doesn't help you in any way at this hotel.

If your company books for you, and they don't use an Amex Platinum (or Centurion) card to book, it's unlikely you will get any FHR benefits.

The Exec Club thing is not a Fine Hotels and Resorts benefit. Unless you manage to get upgraded to a Club level room, which I believe is something that most hotel chains do not do for Fine Hotels and Resorts bookings.

If you book more than 1 room with your Platinum card, at a hotel that is part of Fine Hotels and Resorts, then you will get benefits for both rooms. American Express allows up to 3 rooms on a single booking to get the benefits.