I must reply that, after I followed up with Customer Service (twice, no reply!) I emailed the hotel directly and they did honor the competing rate.
Sofitel Hamma Garden Algiers
DZD 27,100 per night.
Also, as a Platinum member, they have already upgraded me to a Club Room with breakfast included, so that is great!
I just wish the actual Best Price Guarantee program (at the Corporate Level) wasn't so difficult to use.