Seems like from that it's just framework construction. It may have the same internal structure as an ontology, but to say the statements have any external correspondence (to the metaphysical; I'm using 'external' loosely) would require an extra step.

I can set an ontology where `thingamajiggers` are the only entity (so I guess the only truth condition for '∃x P(x)' is that P(x) is a thingamajigger), and I guess if you want to you can say I'm doing metaphysics at that point, though it does seem a little pointless to do so.