(As with all the other entries today, just pretend it has the Old Gods watermark.)
It's not like Y'Shaarj was ever intended to be played competitively. But it's so slow, it's difficult to use even in a fun deck. As much as I'm enjoying the doubled end-of-turn effects and the negative battlecries, what I really want with my card is some good old-fashioned Rush. This card can bypass taunt too - but, sorry, no face damage - and if you summon a minion with charge, the random attack will count as their first-turn attack. Up to and including Y'Shaarj, here's just some of the ways this card could entertain and infuriate your friends:
Bring back that Grim Patron synergy, with a little bit of RNG thrown in - but hey, if their board is full of 1-2 attack minions, you've got nothing to fear.
Combine with clumsy minions. Who knows what will happen?
Possessed Villager, Twilight Summoner, or Mounted Raptor, anyone? Maybe even a Harvest Golem? If you're playing wild, don't forget the Shredders. Actually, even Loot Hoarder or any other deathrattle could get utility out of this.
Don't forget that the "after" means the battlecry happens first, allowing for a bit more control that way.