Lucas Blackstone
Explorer
Shoving a creature: "Using the Attack action, you can make a special melee attack to shove a creature..." is not the same thing as "A shove is a special melee attack". One kind of shove is definitely a special melee attack. The kind that requires you to use your attack action. However, nothing is said about the kind of shove that requires you to use your bonus action.
It's the same thing. Shoving a creature is shoving a creature. The difference is that you use have the option to use a bonus action as part of the attack action, instead of one of the attacks ( perhaps the only attack ) granted by the attack action. Nothing suggests that it is no longer a special melee attack.
If the Shoving a Creature rules didn't apply to shoving a creature with the feat then how would you resolve the shove? History skill check vs the targets AC? Flip a coin? There's no reason the rest of the Shoving the Rules section wouldn't apply to the shove. The specifics of the feat only change the action type used. Specific vs General. You don't discard the entire rule for the specific change, just apply the specific change.