Sam Black has been the primary proponent of Anointed Procession-based token strategies in Standard, to the surprise of no one, but the lists he champions are Abzan with Cryptolith Rite and very much focused on maximizing the token synergies therein.
Today's list is interesting in that it moves away from that concept toward a controlling strategy replete with plenty of removal, including four copies of Fumigate, which appears out of place in a deck that also contains Sacred Cat and Anointer Priest.
But as we all know, appearances can be deceiving in Magic, and that is indeed the case here. The controlling plan makes a lot of sense when you consider that every creature in the deck leaves behind either a Clue token or the potential to embalm, and the primary token generators in the deck are a planeswalker in Gideon, Ally of Zendikar and a value-generating enchantment in Hidden Stockpile, both cards that will play well in long games.
With a more linear strategy, you're better able to assemble the pieces quickly and bury your opponent in a pile of tokens and life from Anointer Priest, but you're also forced into trying to do so as often as possible. Sam's lists do now include Angel of Sanctions for some much-needed interaction, but for the most part, the Abzan Tokens deck is focused on its own gameplan.
This deck can buy its time in setting up the engine, using its removal in the early-game and catching up on the tempo loss from casting Anointed Procession on turn 4 with a Fumigate on turn 5. From there, you can start making piles of tokens and easily outpace your opponent in recovering from the sweeper or force them to answer your enchantment, at which point you revert back into the controlling role until you assemble an engine again.
With aggressive decks on the rise in Standard right now, being able to play an interactive game on the early turns is a significant boon for the deck, and you don't lose much in terms of maximizing the power of Anointed Procession. It may look weird on paper, but that's why we play the games.