Gromm is the finisher. His damage will always be game changing when he can push out 12+weapon damage on one turn and be a strong body on the board. The deck you linked seems pretty out of date to me personally, but there are a number of variants and twists everyone will put on control warrior, and it has a certain amount of flexibility. Currently I would say Thaurissan is a waste in control Warrior decks. Without major card draw or regularly full hands it just doesn't seem super reliable, and throwing down a bunch of cards at once can be a liability.
I stopped running Whirlwind, personally. It feels too situational, which can make it a dead pull a lot of the time. I find having double Brawl to be way more valuable, and it's rare that an early board I could sweep with 1/1s would be entirely threatening. For something like Paladins its not bad to bait out buffs on the minions before Brawling even. Whirlwind does little to fight off the early game off many other classes though, so I just rarely feel like it's worth it. I might feel more this way because I run Baron Geddon though.
Nefarian is not really a sub for Alex. Alex can swing the health situation of the game to pull you back up from lethal against rush, or to push enemies down into lethal range off Gromm. Nefarian is the kind of card that holds momentum rather than swinging it.
If you have Gorehowl/Justicar consider using them. I think they're actually really potent as a combo. Using Gorehowl also extends Gromm kill range really far in certain situations.