This was one of my questions when I first booked a flight with Singapore Airlines, and the answer is YES.
The terminal fee in Peso , or its equivalent in US Dollars may not be obviously visible in an itinerary or receipt, but it is already included. I believe it is the Passenger Service Charge [International] in a fare breakdown.
The only one excluded, of course, is the travel tax which currently costs PHP1620.00*. It varies though, but the amount is fixed for the common tourists flying in economy class. The travel tax for a first class flight is PHP2700.00*.
*Subject to change