Watch some of the best rogue players pilot the deck. Many of the minions have charge and thus can do be used more than once, and with the insane amount of bouncing cards you can easily keep minions in your hand and put pressure at the same time.
Honestly I think you need to play some taunt warrior yourself, when I face taunt warrior as pirate I am quiet happy as I have a positive winrate against them. Yes they have removals, but they are expensive and most of them prevent you from playing taunts at the same time, so its constantly a question on whether to push for the quest or keep removing.
Many of the rogues minions actually do both. The murloc that summons taunt can completely shut down aggro, the elemental that freezes can protect your minions and your face. And at the same time bouncing these will further your quest, on top of that you only need to play the same minion 4 times which is very easy to achieve, which Kibbler also comments on in the video.
Yes quest warrior is very strong, but simply getting the quest done doesnt automatically win you the game. Especially if your playing against aggro decks.