To start with, you probably didn't pay a "Best Price Guaranteed" rate. To use the BPG scheme, you need to book a hotel via one of the approved channels first, then find a cheaper offer on a third-party website and submit your request. Not the other way round.
Also, the BPG rate should be 10% or 25% cheaper than the third-party booking.
In principle, if you booked your stay directly with the hotel, you should get the points and the benefits.
But perhaps they used an usual rate that is not eligible for points (without informing you properly).
I'd ask the hotel to explain what rate was used for your new booking and then try to reason/argue with them (again) so that you get your points.