Lucas Blackstone
Explorer
Ah contraire! The rules don't define shoving as a special melee attack. Instead they define a special melee attack you can make while using the Attack action to shove a creature. The rules actually do not define anything about a shove that is not done while using the Attack action.
That's what makes this question so interesting!
They do define Shoving a Creature. The feat makes an exception to the normal rule of using the attack action to do so. There is nothing that says it is no longer a special melee attack. The feat does say that you use a bonus action to do it instead of the attack action.
Edit: Hooray, the Crawford said it is an attack too, but I was just going by what was in the book.