How much are noise-related landing costs for a long-range aircraft at Heathrow?
As DeltaLima states, the 787 is a Chapter 4 aircraft.

Directly under the table in your question is another table listing the requirements for each category.



So the categories are based on the certified Chapter, and the margin to Chapter 3 standards. Based on these values, the 787 would be categorized as Chapter 4 Low.

You can look up aircraft in the NoisedB here. Each aircraft is tested for its noise margin. I looked at ID:BOEING_14816, which is a 787-8 powered by a GEnx-1B. It has a noise margin of 30.9, which is compared to the Chapter 4 standard. From looking up a Chapter 3 aircraft like a 747-400, it can be seen that the cumulative reduction between Chapter 3 and 4 is 7.3 EPNdB. I did not see any aircraft that would be above the Chapter 4 Low levels, and most are in the "30 or more" category.