I wonder if this is a recent thing or something. I haven't visited the Philippines but IRL haven't heard Filipinos speak with this accent, neither did Filipino friends ~15 years ago (instead sounding more like the unadjusted Filipino example from the website here).
Oh. Just to be clear I'm comparing its closeness to other primary English speaking countries.
There absolutely is still a local language influence.
I think that the accent that is most closest to is American.