Yes, the attack would bypass that reistance
Creatures that say this only resist B-P-S damage types
Damage Resistances bludgeoning, piercing, slashing from nonmagical attacks
When a statblock says this, it means that the creature only is resistant to the bludgeoning, piercing, and slashing damage types from nonmagical attacks. Since force damage is its own damage type, it ignores this statement completely and affects the creature like normal (no resistance).
The next time you hit that creature on this turn with a weapon attack, all damage dealt by the attack becomes force damage
The fact that this ability changes all damage to the force type before damage is inflicted means that the weapon doesn't matter here, it just counts as force damage no matter what.
The force damage would bypass the resistance even without the B-P-S phrase
In the Basic Rules in the section detailing the different damage types, force damage is described as follows:
Force. Force is pure magical energy focused into a damaging form. Most effects that deal force damage are spells, including magic missile and spiritual weapon.
Which means that any force damage should be automatically considered to be magical regardless of the source. See Does Force damage count as magical if the feature causing it doesn't? for more discussion on that case.
Thus, even a creature resistant to all non-magical attacks would still not be resistant to the Planar Warrior's attack.