The article claims Kelly's "81-34" record "doesn’t factor in the 21 victories redacted by the NCAA for impermissible academic help."
The only way to get to 81 is to count the 21 vacated wins. Just pretend that it didn't happen. So, yes, the cited record does factor in the 21 vacated victories.
And the only way to get to 34 is not to count one of the losses, presumably the loss in the 2012 BCS championship game (we can't mention participation, I think, but the loss shouldn't be removed from our totals).
Brian Kelly is 60-35. He's nowhere near Notre Dame's great coaches by any measure, except perhaps tenure. And he shouldn't be close in that respect either, but our esteemed leaders are willing to overlook anything and everything for our guy Bri.