No: Duterte's lockdown on Metro Manila due to COVID-19 does not impact non-Filipino citizens traveling from Metro Manila to somewhere else.
I found the official reference: President Duterte's address to the nation on coronavirus actions on 2020-03-11.
The exact passage regarding air travel can be found at
Land, domestic air and domestic sea travel to and from metro manila shall be suspended beginning March 15 2020 and to end on April 14 2020, subject the daily review by the inter-agency task force [Inter-Agency Task Force of Emerging Infectious Diseases (IATF-EID)].
The French embassy in Manila confirmed this information on 2020-03-12.
I have reported the Reddit post mentioned in the question to the sub's mods for spreading incorrect information.
Now the question is whether there will be any flight available: What percentage of international flights departing from Manila (MNL) are canceled due to Duterte's COVID-19 lockdown on Metro Manila from 2020-03-15 to 2020-04-14?