I'm not sure if I would characterize it as a monarchy (that would be more befitting of North Korea or Turkmenistan), but it clearly shares parallels with other countries in that region in which political parties tend to be vehicles for elite families.

In Pakistan, you have the Bhuttos and Sharifs. In Bangladesh, you have the Sheikh-Wazed and Zia families. In Philippines you have the Marcos and Aquino families. If one of those families conclusively defeated the other, they would indeed look suspiciously monarchical.

Duterte was a bit of an oddball because he was able to break this duopoly. But just as Pakistan's Imran Khan has been replaced by another Sharif, we're seeing these elite families retake the Philippines as well.

I suppose if Aquino's son was the last President, making Marcos' son the next President doesn't seem that objectionable. However, it isn't a total counter-revolution against Duterte, since both Marcos' party and Vice President are both part of the Duterte faction. Whether Marcos has effectively puppetized the Duterte family, channeling their populism into serving establishment ends, or whether the Duterte family have puppetized Marcos, remains to be seen.

Duterte's daughter quite predictably screwed it up, since she would have sailed into the Presidency easily to continue his legacy if she didn't hesitate because she needed time to bring up kids or whatever, time which she all of a sudden no longer needs. But by the time she decided to enter the election, people already had their minds made up on Marcos.