The relevant criteria is that the object 'has sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a hydrostatic equilibrium (nearly round) shape'. Not that it is 'nearly round', and not that it is round through isotropic pressure.

The phrase is perfectly adequate to deal with any object in the solar system about which we already have sufficient information. But it is not (as with many scientific definitions) entirely precise. If we come across a case that will require more precision, then the definition will be refined (like the current refining of the definition of lunar latitude and longitude).

One of the bits of imprecision relates to 'rigid body forces'. Does this mean such forces actually present in the object, or does it mean any conceivable rigid body forces that might be present in an object of such size and/or mass?

Then there is the practical question of determining things near the boundary. Should give a few postgrads a subject for there theses! But any definition always has measurement difficulties near the boundary (unless it's so wide it has no boundary).